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Today:
Coming Up:
• Review Quiz 2 Problems
• Lecture on Section 2.4: Word problems!
• NOTE: This homework is due at the beginning of the next
class session.
Coming up at the next three class sessions:
1. Lecture on Section 2.5
2. Review for Test 1
3. Test 1
Test 1 on all sections covered this semester up to this
point (including material covered on Quizzes 1 and 2,
plus sections 2.4 and 2.5)
Gateway Quiz Retake Facts
• MUST pass with 100% to pass Math 10
• So far: Two attempts to pass in class
– If not passed during one of those two attempts:
• One attempt per week for rest of semester
– Seven weeks = seven chances to pass
• Outside of class time: scheduled times will be given
today and posted on bulletin boards.
Didn’t pass your Gateway Quiz?
Here are the next steps:
• Go over the incorrect answers on your previous
attempts with a TA (and get their signature) in
the Math TLC Open Lab (JHSW 203).
• Take another Practice Gateway Quiz.
– Go over any incorrect answers on the practice
attempts with a TA in the Math TLC Open Lab
• Have a TA in the Math TLC Open Lab sign you
up for a retake time
Gateway Quiz Retake Times
(One new attempt allowed per week, beginning March 20)
During your 11:15am Lab hour
•
•
•
•
Mondays
Tuesdays
Wednesdays
Thursdays
SIGN UP IN THE MATH TLC OPEN LAB!
Online Quiz 2 Results:
•Average class score after partial credit: XX.X%
•Commonly missed questions: # _________________
Grade Scale
Grade
A
A-
B+
B
B-
C+
C
Points
≥ 925
≥ 900
≥ 875
≥ 825
≥ 800
≥ 775
≥ 725
≥ 700
< 700
% Score
≥ 92.5
≥ 90
≥ 87.5
≥ 82.5
≥ 80
≥ 77.5
≥ 72.5
≥70
< 70
C-
F
•If you got less than 70% on Quiz 2, make sure to go over your
quiz with me or a TA sometime today or tomorrow to help you
prepare for the upcoming midterm test.
Please
CLOSE
YOUR LAPTOPS,
and turn off and put away your
cell phones,
and get out your notetaking materials.
Section 2.4:
Application Problems:
General strategy for problem solving:
1) Understand the problem
•
•
•
Read and reread the problem
Choose a variable to represent the unknown
Construct a drawing, whenever possible
2) Translate the problem into an equation
3) Solve the equation
4) Interpret the result
•
•
Check solution
State your conclusion
Example 1:
The product of twice a number and three is the same as
the difference of five times the number and ¾. Find the
number.
Understand
- Read and reread the problem.
- Choose a variable to represent your unknown.
If we let x = the unknown number, then
“twice a number” translates to 2x,
“the product of twice a number and three” translates to 2x · 3,
“five times the number” translates to 5x, and
“the difference of five times the number and ¾” translates to 5x - ¾ .
Example (cont.)
Translate
The product of
twice a
and 3
number
2x
·
3
the difference of
is the same as
=
5 times the
number
5x
and ¾
–
¾
Example (cont.)
Solve
2x · 3 = 5x – ¾
6x = 5x – ¾
(simplify left side)
6x + (-5x) = 5x + (-5x) – ¾ (add –5x to both sides)
x=-¾
(simplify both sides)
Now CHECK your answer (see if both sides produce the same
answer when you put -3/4 in place of x):
Left side: 2x·3= (2·-3/4)·3 = -6/4 · 3 = -3/2 · 3= -9/2
Right side: 5x – 3/4 = 5·3/4 – 3/4 = -15/4 – 3/4 = -18/4 = -9/2 
Consider the difference between the last problem:
The product of twice a number and three is the same as
the difference of five times the number and ¾. Find the
number.
Equation: 2x · 3 = 5x – ¾
(Answer = -3/4)
And this problem:
Twice the product of a number and three is the same as
five times the difference of the number and ¾. Find the
number.
Equation: 2(x · 3) = 5(x – ¾)
(Answer = -15/4)
Example
A car rental agency advertised renting a Toyota Prius for
$25 per day and $0.20 per mile. If you rent this car for 2
days, how many miles can you drive on a $100 budget?
Understand
Read and reread the problem.
Just to get an idea of what’s going on in this problems, let’s start by
considering what the cost would be if we were to drive a total of 100
miles over the 2 days.
In this case our equation for the total cost would come from taking
twice the daily rate and adding the fee for mileage to get
2(25)
+
0.20(100) = 50.00 + 20 = $70.00.
This gives us an idea of how the cost is calculated, and we also now
know that if we have $100 to spend, we can drive more than 100 miles.
Example (cont.)
Translate
Daily costs
So to generalize this specific example of
100 miles, if we let x = the number of
miles driven, then 0.29x = the cost for
mileage driven.
mileage costs
plus
2(25)
+
maximum budget
is equal to
0.20x
=
100
To do this problem without a calculator, we will want to convert
the decimal 0.20 into the fraction 20/100.
Example (cont.)
Solve
2(25) + 20/100 x = 100
50 + 20/100 x = 100
(simplify left side)
50 – 50 + 20/100 x = 100 – 50
20/100 x = 50
(subtract 50 from both sides)
(simplify both sides)
100 20
100
(multiply both sides by 100/20)

x  50 
20 100
20
x = 50∙5 = 250
(simplify both sides)
Example (cont.)
Interpret
Check: If we replace “number of miles” in the
problem with 250, then 50 + 0.20(250) = 50 + 50,
which is equal to our budget of $100.
State your answer: The maximum number of
miles we can drive is 250.
Hint: Start by drawing a picture.
Answer: First piece is 4 inches, second is 12, third is 20.
Example:
The sum of three consecutive integers is 366. What are
the three integers?
Solution:
•Call the first integer x.
•Then what is the next consecutive integer?
•x+1
•And the third one?
•x+2
•So the sum would be what?
•x + x+1+ x+2
• This simplifies to 3x + 3
•And the equation would be what?
• 3x + 3 = 366
Example (cont):
The sum of three consecutive integers is 366.
What are the three integers?
Solution (cont):
•Now solve the equation
• 3x + 3 = 366
• 3x = 363
• x = 363/3 = 121
•Now answer the question:
•First integer = x
• x = 121
•Second integer = x + 1
• = 122
•Third integer = x + 2
• = 123
Example (cont):
The sum of three consecutive integers is 366.
What are the three integers?
Now check your solution: (121, 122, 123)
•Are these three numbers integers?
•Yes
•Are they consecutive?
•Yes
•Do they add up to 366?
• 121 + 122 + 123 = 243 + 123 = 366
• Yes
Example:
Now let’s change the problem slightly:
The sum of three consecutive even integers is 366. What
are the three integers?
Solution:
•Call the first integer x.
•Then what is the next consecutive even integer?
•x+2
•And the third one?
•x+4
•So the sum would be what?
•x + x+2+ x+4
• This simplifies to 3x + 6
•And the equation would be what?
• 3x + 6 = 366
Example (cont):
The sum of three consecutive even integers is
366. What are the three integers?
Solution (cont):
•Now solve the equation
• 3x + 6 = 366
• 3x = 360
• x = 360/3 = 120
•Now answer the question:
•First integer = x
• x = 120
•Second integer = x + 2
• = 122
•Third integer = x + 4
• = 124
Example (cont):
The sum of three consecutive integers is 366.
What are the three integers?
Now check your solution: (120, 122, 124)
•Are these three numbers integers?
•Yes
•Are they even?
•Yes
•Do they add up to 366?
• 120 + 122 + 124 = 242 + 124 = 366
• Yes
Reminder:
This homework on Section 2.4 is due at start of next class
session.
You may want to come in to the lab for help on this homework.
Many students find that these problems take a bit longer to figure
out than previous assignments.
Also, please remember to come in to the lab for your
Gateway quiz review and get your worksheet signed,
then sign up with a TA in the open lab for one of the time
slots for this week’s retake.