Download MPM 1D Name: Unit #3: Solving Equations Name: Unit Outline: Date

Unit #3: Solving Equations
Name: __________________________________________________________
Unit Outline:
Date
Lesson Title
3.0 Solving Simple Equations
3.1 Solving Multi-Step Equations
3.2 Simplifying before Solving
3.3 Solving Multi-Step Equations
3.4 Solving Equations with Fractions
PART 1: One fraction
3.4 Solving Equations with Fractions
PART 2: Multiple Fractions
Quiz #1 – Solving Equations (Lessons 3.1 to 3.4)
3.5 Working with Equations and Formulas
3.6 Solving Word Problems
3.7 Solving Ratios and Proportions
3.8 Solving Percent Problems
Quiz #2 – Solving Equations (Lessons 3.5 to 3.8)
3.9 Review of Solving Equations
Unit Test – Solving Equations (Lesson 3.1 to 3.9)
Assignment
Completed
MPM 1D
Name:
3.1 Solving Multi-Step Equations
Multi-Step Opposite Operations
 Use backwards BEDMAS
Given the equations below,
- list the operations that are affecting the variable
- then, list the operations to undo them.
a) 4n + 6 = 38
b)
x
- 9 = -3
4
Operations affecting variables:
Operations to undo:
Solve the equations above.
PRACTICE: Solve, including an organized, well-communicated process.
a) 2x - 10 = 26
d) -7 = 2x – 21
b) 2x + 3 = 21
c) 3x - 2 = 7
e) 27 = 4x - 5
f) –x + 9 = 12
Extension:
If I asked you to solve the equation x2 = 25,
a. What is the inverse operation of squaring a number?
b. What is a solution?
Is there a second solution that works?
Word Problems. Write an equation for each of the following scenarios:
a) The total cost was $50 when a ski pass costs $25 upfront plus $5 per hour for rentals
b) A plant grows 3 cm a day to its current height of 21 cm.
c) A third of a number decreased by 12 is -7.
2
MPM 1D
Name:
Assignment 3.1 Solving Simple Equations
1. Look at the algebraic expressions and equations below. Which are expressions? Which are equations?
Explain how you know?
p–4
a) 5x = 65
b) y + 8
c) 3a – 6
d) z + 3 = 9
e) 2
f) 3q – 5 = 19
2. Solve.
a) –3k = 18
e) –2g + 3 = –4
3. Solve
a)
b) b – 3 = 12
c) –c = 3
f) 5s + 3 = 2
g) 
b)
x
4
d) 6w – 4 = –22
=6
h) 3d – 5 = –1
c)
4. Find two solutions for each of the following equations
a) x2 = 81
b) y2 = 144
c) m2 = 86
5. Create a two-step equation that can be solved using opposite operations. The solution to your equation
must be w = -3.
6. Describe the solution to these equations
a) 3x = 0
b) 0y = 2
c) 0z = 0
7. For each situation below, write an equation you could use to solve each problem. Solve each equation.
a) Abba bought 15 DVD’s for $255. She paid the same amount for each DVD. How much did Abba pay
for each DVD?
b) A banquet hall charged $120 for the rental of the hall, plus $14 for each meal served. The total bill
for the banquet was $610. How many people attended the banquet?
8. a) One more than three times a number is 28. What is the number?
b) Four less than five times a number is 31. What is the number?
c) Twice a number increased by seven is 29. What is the number?
d) Seventeen added to three times a number is 53. What is the number?
3
MPM 1D
Name:
3.2 Simplifying Before Solving
Warm Up:
Simplify
a) 3(2m + 1)
Simplify the following expressions, then evaluate
for the given values
a. -5(2x – 1)
if x = 6
c. 8x – 5 – x + 9
if x = 7
d. 2(4m – 3) – 2(m + 5)
if m = -4
b) –6(1 – 3v)
c) –(n + 2)
d) 3(5 + 2g)
Back to the Balance Model
Sometimes a visual helps in algebra.
Build and solve the equations:
Problem
Solve algebraically
Visual
Solve using the balance model
2(x+5) = 14
x=
x=
4
MPM 1D
Mental and Formal Checks
Name:
A mental check is a quick way of determining if your answer is correct. Simply substitute your answer
back into the original equation and then evaluate. It is NOT solving for the variable.
Practice Problem:
Mrs. Sheppard solved 5x + 6 = -9 and said that the answer was -3. Check to see if she is correct without
actually solving….
A formal check is more mathematical and elegant. It involves following rules agreed upon by all
mathematicians to prove (beyond a reasonable doubt) that the answer is correct.
Practice Problem:
a) Perform a formal check on the equation 6w – 4 = –22 to determine if w = -3 is the correct answer.
Formal Check Instructions:
1) State what you are checking
2) State what the left side of the equation equals
3) State what the right side of the equation equals
4) Substitute the value
5) Simplify each side of the equation SEPARATELY
6) Make your concluding statement
b) Solve the following equation 5(k + 3) – 2(4k + 7) = -5, then perform a formal check.
5
MPM 1D
Name:
Practice Problems:
1. A rectangle has a length of 7x – 4 and a width of 8 – 2x. The perimeter of the rectangle is 38 cm. Determine
the length of each of the sides.
2. The figure below has a perimeter of 62 m. Determine the length of side AB. Show your work.
6
MPM 1D
Name:
Homework 3.2 Simplifying before Solving
1.
2.
3.
Solve.
a) 6x + 3 + 2x = 19
c) 4a + a + 9 = 44
e) 2y + 4 + 3y = 9
b) 10m – 3m + 8 = 43
d) 15 – 3b + b = 3
f) 7f – 12 + f = 20
Solve.
a) 4(x – 3) – 3x = – 7
c) 12 = 4(d + 2) + 3 – 5d + 9
b) 2(a – 8) + 3(a + 6) = 17
d) 2(3t + 5) – 4(2t – 1) = 6
Solve, then perform a formal check.
a) 2m + 1 – m = 4
b) 5(k + 3) – 2(4k + 7) = -5
8
3x
4. The perimeter of the triangle (on right) is 40 cm. Find the value of x.
x + 12
5. The perimeter of an isosceles triangle is 21 cm. The length of each equal side is triple the length of the
base. Find the side lengths of the triangle.
6. Translate each sentence below into an equation and solve for the number described.
a) Three times the sum of a number and four is 45.
b) The sum of four times a number and six times a number increased by eleven is 51.
c) Four less than three times a number increased by six times the same number is 32.
d) Three times a number subtracted from 4 less than seven times a number is 28.
7. Solve the equations
1
1
1 1
a) x - x = +
2
3
6 4
b) 3x 2 - 2 = 25
Enrichment: Solve the equation 2 ( x +1) -1 = 71
2
*hint: what is the opposite of squaring (x+1)?
7
MPM 1D
Name:
3.3 Solving Multi-Step Equations
Warm Up:
* Remember to simplify before solving…..
(a) 3k – 9 = 6
(b) 4 – 2x + 6 – 3x = - 5
Variables on Both Sides
How would you solve the following using opposite operations.
b) 6a + 2 = 9a + 4
(c) 5(x + 4) = 40 – (-5)
STEPS:
1.
2.
3.
4.
5.
3a + 4 = 2a – 6
Practice Problems:
1) A square and an equilateral triangle are pictured below. The square and the triangle have the same
perimeter. What is the value of x?
8
MPM 1D
Name:
2) Solve the following equations
1
b. 2( x  3)  (4 x  12)
2
a. 3( x  2)  5  2( x  3)
3)
A health club charges nonmembers $2 per day to swim and $5 per day for aerobic classes. Members
pay a yearly fee of $200 plus $3 per day for aerobic classes. Write and solve an equation to find the
number of days you must use the club to justify a yearly membership.
9
MPM 1D
Name:
Homework 3.3 Solving Multi-Step Equations
1. Solve
a) 3b + 4 = 2b + 6
c) 2x + 4 = 5x – 5
e) 6h – 5 = 2h + 3
2. Solve
a) 2 + (4h – 1) = 11 + 2h
c) 2(d + 6) = 9(d – 1)
3.
Solve
a) 4s + 3 – s = –6
c) 5 – (c + 3) = 4 + c
4. Solve, then perform a formal check:
b) 7p – 18 = 3p – 2
d) 8g + 3 = g + 10
f) 4m – 9 = m + 7
b) 8 – (2g + 3) = 3g – 5
d) 5(3r – 7) + r = 3(r – 3)
b) p – 3 + 2p – 9 = 0
d) 3(4d – 7) – 6 = 2(d + 2) – 1
6 – 3(4k + 1) = 5 + (10 – 8k)
5. A regular polygon has equal sides. In the diagram below, the perimeter of the regular hexagon is equal to
the perimeter of the equilateral triangle.
3x-2
5x+8
a)
b)
Determine the value of x.
What is the perimeter of the equilateral triangle?
6. Solve the equation
1
3
1
x+ = x2
4
2
Enrichment
a) Show that the equation 2x -3 = 4 + 2x has no solution. Why do you think this happens?
10 - 6x
b) Show that the equation
= 5 - 3x has an infinite number of solutions. Why do you think this
2
happens?
10
MPM 1D
Name:
3.4 Solving Equations with Fractions
Part 1: One fraction
Warm Up:
Evaluate
(a)
3
5

4
 3  2 
(b)      
 5  3 
3
 2 
(b)     
 6 
1

8
(e)
3 1

8 4
(d)
(f)
1  4
  
4  5
2  4 1
   
3  9 5
Solving Equations with Fractions
Solve:
Method 1: (distributing the ¾)
Method 2: (avoiding fractions)
11
MPM 1D
We can handle fractions!
If there is
Name:
only 1 fraction in the equation:
1st: Remove constants using opposite operations (Addition/Subtraction step)
2nd: Undo division using opposite operations *note.. MUST BE APPLIED TO EACH TERM
3rd: Undo multiplication using opposite operations (if needed)
1)
x
 9  11
5
2)
x
 4  5
3
3)
2
x  16  64
3
Independent Practice:
 Step 1: Remove constants
 Step 2: Multiply every term in the equation by the denominator
 Step 3: Reduce any leftover fractions
 Step 4: Solve for the variable using opposite operations
1)
x
 10  1
4
2)
x
- 8 = 15
7
3)
12
3
x7  8
4
MPM 1D
Name:
Homework 3.4 Part 1 - Solving Equations with a fraction
13
MPM 1D
Name:
3.4 Solving Equations with Fractions
Part 2: Multiple fractions
If there are 2 or more fractions in the equation:
Method 1: (removing fractions)
1st: Find the Least Common Denominator (LCD) of all of
the denominators
2nd: Multiply EVERY term in by the LCD
*Remember to put all (binomials in brackets) before
multiplying!
3rd: Reduce any fractions
4th : Collect like terms
5th: Remove constants (use opposite operations)
6th: Simplify and solve!
LCD: ___
1)
x
5

x
7
4)
x  3
6
LCD: ___
2)
 12
** USE BRACKETS!

x  25
5
Method 2: (creating fractions)
1st: Find Least Common Denominator (LCD)
2nd: Rewrite each fraction with LCD
3rd: Collect like terms
4th: Remove constants (use opposite operations)
5th: Use opposite operations to undo division
6th: Simplify and solve!
7x
10

x
5
LCD: ___
3
2

LCD: ___
 4
5
4
3)

x
2
LCD: ___
5)
☼ Make sure you distribute and watch out for the negative!
14
x  5
2

x  1
2

x  1
3

7
6
MPM 1D
Name:
Challenge Questions:
Follow the four steps to solve the following equations. Show all of your work!
1)
5x x 51


8 12 24
2)
x  3 3x

7
5
10
3)
x 4 x
 6
4
3
4)
y5
 4  16
3
15
MPM 1D
Name:
Homework 3.4 Part 2 - Multiple Fractions
Enrichment: Solve the following equation. *hint: what is the common denominator of 2 and x?
16
MPM 1D
Name:
3.5 Working with Equations and Formulas
The following formula can be used to convert
temperatures from degrees Celsius, °C, to degrees
Fahrenheit, °F:
9C  160
F
.
5
a) Use the formula -7°C to degrees Fahrenheit.
Formulas are often used in both math and
science, write down as many formulas as you
can remember
b) Use the formula to find out at what temperature
F = C.
LESSON:
Rearranging Formulas
When working with math, (whether in Chemistry class, Physics class, Business class, etc), you will need
to rearrange equations to make them easier to work with. Rearranging equations follows the same rules
as solving equations, but there will be more than one variable to choose from.
Practice Problems: Rearrange each formula to isolate the variable indicated.
bh
A
a)
for h
b) 2y + 3x = 30
for y
2
c) SA = 2p r 2 + 2p rh for h
2
d) V =  r h
17
for r
MPM 1D
Name:
Standard Form of an Equation
Standard form is an agreed upon set of rules used to rearrange equations. Equations in standard form
must….
Practice Problems: Rearrange each equation into standard form.
a) y = -3x + 7
b) 9x -8z = -3y +10
4
c) y = - x + 3
5
d)
2
1
x+ y=2
3
5
Challenge Questions: Rearrange in terms of the given variable
a) Ax + By + C = 0
for y
b) a2 + b2 = c 2
18
for b
MPM 1D
Name:
Homework 3.5 Working with Equations and Formulas
1. Rearrange each formula to isolate the variable indicated.
a. P = 4s
for s
b. I = Prt
for P
c. A 
bh
2
e. d = st
for b
d. P = 2l + 2w
for l
for t
f. V =  r 2h
for h
2. Solve the following equations for y:
a. x + y = 10
b. y + 2x = 4
d. 3 + y = 8x
e. –y – 5x = -6
c. –6x = 2y + 3
f. 10y – 10 = x
3. Rearrange the following equations to standard form.
a. 4x + 6y = 8
b. –6x – 7y – 9 = 3
c. x = 8y – 4
d. 9y = -5x + 6
e. 7y = 4x
f. 4x – 8y + 10z = 2x
3
2
1
1
g. 5x –7y = 2x –19y – 30 h. y = - x + 5
j. x + y = 4
3
4
2
4. Solve each formula for the variable indicated.
a. V  r 2 h for h
mv 2
b. C 
for r
r
c. S 
dN
12
for d
1 2
gt for g
2
gm1 m 2
e. F 
for m1
d2
d. s 
f. A  P  Pr t for t
Enrichment: Solve each formula for the variable indicated.
a) A  P  Pr t for P
b)
a c
= for a
b d
19
b)
a c
= for d
b d
MPM 1D
Name:
3.6 Solving Word Problems
Warm Up
1. Determine the next two consecutive integers in
each case.
Write down words that mean the following
mathematical operations.
Addition
(a) -5, -4, -3, _____, _____,
(b) 12,13,14, _____, _____, _____
Subtraction
(c) x, _________, _________, _________
2. Determine the next three consecutive even
integers in each case.
Multiplication
(a) -18, -16, -14, _____, _____, _____
(b) 20,22, _____, _____, _____,
Division
(c) x, _________, _________, _________
3. Determine the next three consecutive odd
integers in each case.
Equals
(a) -13, -11, -9, _____, ______, _____
(b) -5, -3, -1, _____, ______, _____
(c) x, _________, _______, _______
MY PROBLEM SOLVING APPROACH: (G.R.A.S.P., Read/Think/Solve/Explain , R.U.M.O.R.)
20
MPM 1D
Name:
STEPS IN SOLVING WORD PROBLEMS
1. Define the variable – using a “let” statement.
2. Create an equation that expresses the information given in the problem’s scenario.
3. Solve your equation using algebraic methods.
4. Consider if your answer is reasonable.
5. Write a concluding statement, be sure to include units.
6. Check your answer with the conditions given in the problem.
Practice Problems:
1) Quinn was shopping at a used book sale where all books were selling at the same price. He bought six
science fiction books and eight mysteries. He also decided to buy a poster for $2.40. In total, Quinn spent
$8.70. What was the price of a single book?
2) Oberon Cell Phone Company advertises service for 3 cents per minute plus a monthly fee of $29.95. If
Parker’s phone bill for October was $38.95, find the number of minutes he used.
21
MPM 1D
Name:
3) Rachael and Sabine belong to different local gyms. Rachael pays $35 per month and a one-time
registration fee of $15. Sabine pays only $25 per month but had to pay a $75 registration fee. After
how many months will Rachael and Sabine have spent the same amount on their gym memberships?
4) Ella has an older sister and a younger sister. Her older sister is one year more than twice Ella’s age.
Ella’s younger sister is three years younger than she is. The sum of their three ages is 26. Find Ella’s
age.
5) Find two consecutive integers such that their sum is 89.
22
MPM 1D
Name:
6) Find three consecutive even integers such that the sum of twice the first and three times the third
is fourteen more than four times the second.
Challenge: Andy sold watches for $9 and alarm clocks for $5 at a flea market. His total sales were
$287. People bought 4 times as many watches as alarm clocks. How many of each did Andy sell?
What were the total dollar sales of each?
23
MPM 1D
Name:
Assignment 3.6 Solving Word Problems
1. Together Barry Sullivan and Mitch Ryan sold a total of 300 homes for Regis Realty. Barry sold 9
times as many homes as Mitch. How many did each sell?
2. Wade purchased three videos and one music CD. The CD cost Wade $12.99. If he paid the same
amount for each video and spent a total of $42.96, how much did each video cost?
3. At the market, Xiang bought a bunch of bananas for $0.35 per pound and a frozen pizza for $4.99.
The total for Xiang’s purchase was $6.04 without tax. How many pounds of bananas did Xiang buy?
4. Yamir went to the store to buy gardening supplies. A bag of dirt was $3.99 and tulips cost 75 cents
per bulb. He bought one bag of dirt and some tulip bulbs and spent a total of $12.24 without tax.
How many bulbs did Yamir buy?
5. Zoe is comparing two local yoga programs. Yoga-Weigh charges $90 dollars a month and a
registration fee of $35. Essence of Yoga charges $80 per month with a $75 registration fee. After how
many months will the two schools charge the same amount?
6. Abbey and Blanca are playing games at the arcade in the mall. Abbey has $20 and is playing a
game that costs 50 cents per game. Blanca arrived at the arcade with $22 and is playing a game that
costs 75 cents per game.
(a) After how many games will the two girls have the same amount of money left?
(b) How much money do they have at this point?
7. The length of a rectangular garden is three feet more than twice its width. If the perimeter of the
garden is 114 feet, then what is the width of the garden?
8. Find two consecutive integers that have a sum of −67.
9. Find three consecutive even integers such that their sum is 42.
10. Find three consecutive odd integers that have an average of 13.
11. Find two consecutive even integers such that twice the smaller diminished by twenty is equal to
the larger.
12. Find three consecutive odd integers such that twice the sum of the first and third exceeds the
second by fifteen.
13. Find three consecutive integers such that the sum of twice the second and three times the third is
five less than six times the first.
14. Explain why the sum of two consecutive integers must always be odd.
15. The cost of a pen is 3 times the cost of a pencil. The cost of 4 pencils and 3 pens is $9.75. What is
the cost of a pencil? What is the cost of a pen?
24
MPM 1D
Name:
3.7 Solving Ratios and Proportions
Warm Up:
Ratio – a comparison of two numbers by divison.
Four out of five cars were red. Write this ratio in three different ways:
Rate – a ratio of two measurments with different units.
Mr. Underwood ran 400 yards in 80 seconds. Write this as a rate
Unit Rate – a rate in which the denominator is 1
In example above, write Mr. Underwood’s unit rate
Jill is selling cookie dough. Three tubs cost
$22.50. How much will 8 tubs cost?
A basketball player made 12 free throws in 4
games this year. About how many free throws
would you expect the player to make in 100
games?
25
MPM 1D
Name:
Proportion – an equation that shows that two ratios are equivalent.
Fred got two out of every three questions right. If there were six questions, Fred got four questions
correct.
2 4
= is a proportion
3 6
Note: Reciprocal of proportions are also equal
Solving Proportions
Solve each proportion…..Remember how we solved with fractions:
Think LCD and opposite operations.
*hint: easier if variable is in the numerator
x 4
6 4
a) 
b) x = 5
c) =
5 7
7 x
9 6
d)
9
6
=
5 x +1
Applications – Part to Part Problems
Practice Problems:
1. An employee making $28; 000 receives a raise of $1000. All other employees in the company are
given proportional raises. How much of a raise would an employee making $32000 receive?
2. A train travels at a steady speed. It covers 15 miles in 20 minutes. How far will it travel in 7 hours,
assuming it continues at the same rate?
26
MPM 1D
Name:
3. In the United States, 21 out of every 100 people are under the age of 15. In a town of 20,000
people, how many people would you expect to be under the age of 15? 15 and over? Would you
expect these ratios to be equivalent in every town in the United States?
Applications – Part to Total Problems
Practice Problems:
1. The ratio of red marbles to blue marbles is 5 to 7. If there are 156 marbles total, how many red
marbles are there?
2. Carl, Rani and Katy win a prize of $600. They decide to share the prize in the ratio of their ages.
Carl is 15, Rani is 10 and Katy is 5. How much does each of them get?
27
MPM 1D
Name:
Assignment 3.7 Solving Ratios and Proportions
1. The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can
they make in 15 minutes?
2. A typist can type 120 words in 100 seconds. At that rate, how many seconds would it take her
to type 258 words?
3. Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would
be needed if you use 100 ml of yellow paint?
4. A car traveled 130 miles at a constant speed moving for two hours along a highway.
What is the distance traveled by the car if it was moving for 4.5 hours at the same speed?
5. The ratio of boys to girls in a school is 4 to 3. If there are 195 girls in the school, then how ma
ny students are in the school?
6. The ratio of girls to boys is 13:11 in a school. If there are 1968 students, then how many girls
are in the school? How many boys are in the school?
7. A school has 3460 students. If the ratio of boys to girls is 31 to 44, how many more girls are
there in the school?
8. To make standard concrete, gravel, sand and cement are mixed in the ratio 5:3:1. I wish to
make 180 tonnes of concrete. How much gravel, sand and cement must I purchase?
9. The recommended disinfectant to water ratio is 1: 20. How many mL of concentrated
disinfectant are required to make a 9 L bucket of mixture?
10. Joe and Bob share the cost of a video game in the ratio 3:7.
a. What fraction does each pay?
b. If the game costs $35, how much does each pay?
c. If Joe pays $12, how much does Bob pay?
d. If Bob pays $42, what is the price of the video game?
11. A student council collects aluminum pop tabs to raise money to purchase a wheel chair. A
company buys the pop tabs for $0.88 per kilogram. If 1267 pop tabs have a mass of one
pound, how many pop tabs are needed to purchase a wheel chair worth $1500? (Hint 1
kilogram = 2.2 pounds)
28
MPM 1D
Name:
3.8 Solving Percent Problems
Warm Up:
What does the word percent mean?
When is percent used outside of math class?
Complete the table below:
REDUCED
FRACTION
DECIMAL
In her math class, Samantha’s two most recent
quiz grades are 29/35 and 22/26. Which quiz
grade represents the better score?
PERCENT
155%
9
16
0.06
43.2%
Estimating percent is very helpful when shopping.
a) Estimate the amount that you should tip on a bill of $45.98.
b) Estimate the amount of tax on a purchase of $134.50.
29
MPM 1D
Name:
Percent Review
A percent is a ratio between two quantities in which the second quantity is always 100.
84% means
or 0.84.
You need to have a solid working knowledge of percents, not only for success in this course, but also
because percents are used in so many areas in our lives outside of school, such as sports statistics,
taxes, wage increases, and sales commissions.
Because finding a percent involves work with equivalent fractions, many percent questions are easily
handled by solving a proportion of the following type:
part percent
=
total
100
is
%
=
of 100
Note: It may be helpful to think of the ratio
“part/total” as “is/of.”
The whole is often preceded by the word “of” in the
problem.
The part (or percentage) often precedes the word “is”
in the problem.
Practice Problems: Answer each of the following questions by setting up an appropriate proportion
and solving for the unknown. Round answers to the nearest tenth, where appropriate.
(a) What number is 18% of 200?
(b) 42 is what percent of 98?
(c) 6% of 240,000 is what number?
(d) 12% of what number is 1044?
30
MPM 1D
Name:
Percent Word Problems: Answer each of the following exercises by setting up and solving an
appropriate proportion.
1) Tanisha is about to sell her house for $315,000. Her real estate broker will expect to receive a 6%
commission for all of her hard work in finding Tanisha a buyer for her house. How much money will
the real estate broker expect to be paid once Tanisha’s home is sold?
2) Quinn decided to raise all of the prices in his store by 4%. What is the new price of an $8.25 item
after the 4% increase?
3) Discount Dave’s is having an end of summer clearance sale. All items are 60% off. What is the sale
price of a flat screen TV normally priced at $3499? What is the final cost after 13% sales tax is added
on?
Bonus: Sheila claims that if you increase a number by 10% and then decrease the result by 10%, you
are right back where you started. Show that Sheila is incorrect by using a specific numerical example.
31
MPM 1D
Name:
Assignment 3.8 Solving Percent Problems
1.
15% of what number is 24?
2.
What percent of 300 is 0.75?
2.
What is 30% of 95?
4.
33
5.
What percent of 75 is 375?
6.
What is 0.08% of 3200?
7.
What is
1
% of 5?
2
8.
2.5% of what is number 12.5?
1
3
% of what number is 150?
9. David has $425 worth of items in his shopping cart. He receives a discount of 30% for the items at
the checkout. If he then has to pay an 13% sales tax, what is the final amount that David paid?
10. During a recent clothing sale, a department store offered a discount of 30% off any jacket. Maria
paid $45.50 for a jacket after the discount. What was the original price of the jacket?
11. At the Fine Leather Emporium, a $500 leather jacket is on sale for $350. What is the percent of
the discount?
12. A math test was passed by 88% of those students who took the test from a certain school. If 792
students passed the test, then how many students did not pass the test?
13. A survey of teenagers from a certain town ages 14 to 18 was taken to see how typical it is for a
teenager from that town to carry a cell phone. 88 of the teens surveyed responded that they do carry
a cell phone, which represented 80% of the total number of teens surveyed. How many teens were
surveyed?
14. After eating a meal at a restaurant, it is appropriate to leave a 15-20% tip for the waiter or
waitress. If your total bill at a restaurant comes to $118.00, what should your tip be if you decide to
leave a (a) 15%? And (b) 20%?
15. Tammy claims that if you increase a number by 10% and then increase the result by 10%, then
you have increased the original number by 20%. Show Tammy that she is incorrect by using a specific
numerical example.
16. Margie has 8.5% of her weekly paycheck deposited into her retirement account. This week she
had $47.55 deposited into her account. How much was her paycheck
17. Corbett Sprockets Inc. increased its profits by 18% over the past year. If profits last year were
$1,400,800, what are its profits this year?
18. Jason works at a local men’s store and is in charge of pricing new items before they are put on
the rack. He has a shipment of men’s suits that will be marked up 35%. If each suit costs the store
$275.00, what will the selling price be after the mark-up?
20. At the Miracle Plastic Company they had a daily production run of 220,000 units. 1760 of those
units were defective. What is the percentage of those units that were defective?
32
MPM 1D
Name:
Answers
Assignment 3.1
1. Expressions: b, c, e
I know they are expressions because they do not have an equals sign.
Equations: a, d, f
I know they are equations because they each contain an equal sign.
2. a) 6 b) 15
c) 3
d) 3
e) 7
2
f)  1
5
g) 24
h) 4
3
3. a) -5/8
b) -1/10 c) -1/4
4. a) 9 and (-9) b) 12 and (-12) c) approx. 9.3 and (-9.3)
5. answers may vary
6. a) x must equal zero b) there is no solution to this equation c) z can be any number
7. a) 15n = 255; n = 17; she paid $17 for each DVD.
b) 120 + 14n = 610; n = 35; 35 people attended the banquet.
8. a) 3n + 1 = 28; n = 9; the number is nine.
b) 5n – 4 = 31; n = 7; the number is seven.
c) 2n + 7 = 29; n = 11; the number is eleven.
d) 17 + 3n = 53; n = 12; the number is twelve.
Assignment 3.2
1. a) 2
b) 5
c) 7
d) 6
e) 1
2. a) 5
b) 3
c) 8
d) 4
3. a) 3
b) 2
4. 5 cm
5. 3 cm, 9 cm, 9 cm
6 a) 3(n+4) = 45; n= 11 b) 4n+6n+11 = 51; n= 4
d) (7n -4) – 3n = 28; n= 8
5
7. a) b) x = 3 or x = -3
2
Enrichment: x = 5 or x = -7
Assignment 3.3
1. a) 2
b) 4
c) 3
2. a) 5
b) 2
c) 3
3. a) 3 b) 4
c) 1
4. k = -3
5. a) x = 12 b) P = 204 units
5
6.
2
d) 1
e)
f)
4
c)3n -4 + 6n = 32; n = 4
2
d) 2
d) 3
33
f)
16
3
MPM 1D
Name:
Assignment 3.4
Part 1 :
Part 2 :
A: (1) x=2, (2) y=4,(3) n=4,(4) m=-2 (5) y=-6,(6) y=20,(7)n=-1,(8)p=1,(9)n=15,
(10) x=-4,(11) y=-2,(12) x=1,(13) x=14,(14) x=4,(15) n=-9,(16) x=-2,(17) k=5,(18) x=-9,
(19) x=2,(20) z=2
12
5
B: (1)
or1 hours (2) 20 minutes
7
7
Assignment 3.5
1.
2.
3.
4.
a) s  P
4
b)
P I
rt
c) b  2 A
h
d) l  P  w
2
e) t  d
s
f) h  V 2
r
3
1
a. y = 10 – x b. y = 4 – 2x c. y = -3x d. y = 8x – 3 e. y = 6 – 5x f. y =
x+1
2
10
a. 4x + 6y – 8 = 0
b. –6x – 7y – 12 = 0 c. x – 8y + 4 = 0
d. 5x + 9y – 6 = 0
e. –4x + 7y = 0
f. 2x – 8y + 10z = 0
h. 3x + 4y – 20 = 0
i. 8x + 3y + 6 = 0
2
mv
12 s
V
2s
a. h  2
b. r 
c. d 
d. g  2
N
c
r
t
2
Fd
A P
e. m1 
f. t 
Pr
gm 2
Assignment 3.6
1. Mitch – 30 houses and Barry 270 houses 2. $9.99
3. 3 pounds
4. 11 bulbs
5. 4 months
6. a) 8 games b) $16 left
7. 18 feet
8. -34 and -33
9. 12, 14, and 16
10. 11, 13, and 15
11. 22 and 24
12. 3, 5 and 7
13. 13, 14 and 15
14. 2n + 1
15. $0.75 pencil and $2.25 for a pen
Assignment 3.7
1. 9000 crayons
2. 215 seconds
3. 26.67 ml of red
4. 292.5 miles
5. 455 students
6. 1066 girls and 902 boys 7. 600 more girls
8. 100 tonnes of gravel, 60 tonnes of sand and 20 tonnes of cement
3
4
9. ml of disinfectant and 8 ml of water
7
7
3
7
10. a) Joe pays
and Bob pays
b) Joe pays $10.50 and Bob pays $24.50
10
10
c) Bob would pay $28.00
d) Video game costs $60.00
11. 4 751 123 pop tabs
Assignment 3.8
1. 160
2. 0.25%
3. 28.5
5. 500%
6. 2.56
7.
9. $336.18
13. 110 teens
17. $1,652,944
10. $65.00
14.a) $17.70 b) $23.60
18. $371.25
11. 30% discount
15. Answers may vary
19. 0.8% defective
34
1
or 0.025
40
4. 450
8. 500
12. 108 students
16. $559.41