Download 5-Step Process for Solving Problems

Lessons 5 and 6, Section 1.4
5-Step Process for Solving Problems
1. Evaluate the Problem
• Draw a Picture
• Fill in information in a table
• Identify comparisons, totals, equals, etc.
2. Define Variable(s) and Unknowns
• x=?
• Represent other unknowns using x
3. Develop a Plan
• Write a Formula
• Write a Word Sentence
4. Write an equation from your plan and Solve equation
5. Answer Question (with correct labels)
Emphasize deriving the
equations for each
applied problem.
Examples:
1)
The sum of two numbers is 83. One of the numbers is 11 more than the other.
What are the numbers?
• Variable: Let x = number
x + 11 = other number
• Plan: Number + Other number = Sum
• Equation:
2)
A paddleboat can run 8 miles per hour in still water and the river flows at 3 mph.
How long will it take the boat to go 3 miles upstream?
How long will it take the boat to go 3 miles downstream?
Note: rate upstream = boat – current, rate downstream = boat + current
• Variable: t = time
• Plan: d = rt
1
3)
The second angle of a triangle is 5 degrees less than the first angle. The third
angle is triple the second angle . Find the measurement of the smallest angle.
x = 1st angle
Let the angle that the least is
= 2nd angle
rd
known about equal x . The
= 3 angle
sum of 3 angles inside of a
triangle is always 180°
Plan: Angle 1 + Angle 2 + Angle 3 totals 180 degrees
4)
QVC shopping determines the selling price of a diamonique ring by marking up
the wholesale price by 25% and adding $4.25 for shipping and handling. If a
customer is charged $166.75 for the ring, how much was the wholesale price?
x = wholesale price
= markup
Plan: Wholesale price + Markup + Shipping/handling = Selling price
5)
Find three consecutive odd integers such that the sum of the largest, twice the
middle, and 3 times the smallest is 50.
x = 1st odd integer
Three consecutive
x + 2 = 2nd odd integer
numbers could be
rd
= 3 odd integer
represented as x, x + 1,
Plan: Largest + Twice middle (2nd) + 3 times smallest (1st) = sum
and x + 2.
Three consecutive evens
or 3 consecutive odds
would be represented as x,
x + 2, and x + 4; since the
smallest to the middle has
a difference of 2 and the
middle to the largest has a
difference of 2.
2
6)
A piece of wire 100 centimeters long is to be cut into 2 pieces and each piece is to
be bent to make a square. The length of each side of the larger square is 1 cm
more than the length of each side of the smaller square. What are the dimensions
of each square?
x = length of side of the smaller square
Perimeter is the distance
x + 1 = length of side of the larger square
(length) around a shape. The
Plan: Perimeter smaller + Perimeter larger = 100
formula for perimeter of a
square is p = 4s, where s is the
length of a side.
7)
Lynn wants to have an average of 80 points on his algebra exams. His first three
exams are 91, 72, and 81 points. What does he need on his fourth exam to keep
his average of 80?
x = score on 4th exam
1st + 2nd + 3rd + 4th
Plan:
= average
4
8)
Julie and Paige have won a total of 43 tennis matches this summer. If Julie won
11 more matches than Paige, how many matches did Julie win?
x = wins for ?
Plan:
wins for Julie + wins for Paige = total matches
3
9)
The width of a rectangular greenhouse is one-fourth its length and its perimeter is
130 meters. Find the length and width of the greenhouse.
Variable:
Plan:
10)
x+3
The height and sides of a triangle are 4 consecutive integers with the height being
the smallest integer and the base the third integer. If the perimeter of the triangle
is 30 inches, find the length of the longest side of the triangle.
x = height of triangle
x + 1 =one side
x + 2 = base
x+1
x
x + 3 = other side
x+2
11)
Perimeter = twice width + twice length
The formula for perimeter
of a rectangle is
p = 2w + 2L
Plan:
In 2002 there were 301 long distance area codes in the United States. This was an
increase of 250% over the number when the area code plan originated in 1947.
How many area codes were there in 1947?
x = number of area codes in 1947
Plan:
Number in 1947 + Increase = Number in 2002
4
12)
The John Hancock Center in Chicago has a rectangular base whose length
measures 65 feet less than twice the width. If the perimeter of the base is 860
feet, what is the length of the base?
13)
The two companies with top revenues in the Fortune 500 list for 2002 were WalMart and Exxon Mobil. Their revenues together totaled $412 million. Exxon
Mobil revenues were $28 million less than Wal-Mart revenues. What were the
revenues for Exxon Mobil?
x=
14)
When
2
of a number is subtracted from 12, the result is 10. Find the number.
3
x = the number
Plan:
Twelve -
2
of number = 10
3
5
15)
At the end of a day, Jeff found that the total cash register receipts at the motel
where he works accounted to $2725. This included a 9% sales tax charged. Find
the amount of the room charge?
x =
= tax
Plan:
Room charges + tax = total receipts
6