Problem Solving

Remember:
~ read the problem several times and look for important information

~ draw a picture

~ define a variable (only one is needed). You may write other expressions using that one variable.

~ write an equation

~ solve the equation algebraically

~ be sure to answer the question completely.

Question 1 A country's flag has 50 stripes on it, one for each province. The number of blue stripes is double the number of white stripes, and the number of gold stripes is ten less than three times the number of white stripes. How many stripes of each color are in this country's flag? Answer 1	Question 2 At one point during a football game, the line for the women's bathroom was twice as long as the line for the men's bathroom. If a total of 39 people were waiting in line, how many men and how many women were there? Answer 2
Question 3 Children's tickets to a museum cost 1/3 as much as adult tickets. If it costs $15 for two adults and three children to visit the museum, what is the price of an adult ticket? Answer 3	Question 4 Zach is seven years older than Alex. In five years, the sum of their ages will be 19. How old are each of the boys now? Answer 4
Question 5 Peg's Pumpkin Patch sells small, medium, and large pumpkins (all the same standard size and weight). A small pumpkin weighs 15 ounces less than a medium pumpkin and a medium pumpkin weighs 50 ounces less than a large pumpkin. If 3 of each size weigh 555 ounces together (9 pumpkins total), how much does one of each size weigh? Answer 5	Question 6 Victor bought 8 CD's for $5 off the original price of each. He paid $63.92 for them. What was the original price of one CD? (Assume that all the CD's were the same price to begin with.) Answer 6
Question 7 Jamie made chocolate chip cookies. She spent t minutes mixing the ingredients, but it took one more than twice that time to bake the cookies. If it took Jamie a total of 22 minutes to make the cookies, how long did it take to mix the ingredients? Answer 7	Question 8 Chris spent a total of 4 hours washing and waxing his pickup truck. He spent two hours more waxing than he did washing. How long did it take to wash the truck? Answer 8
Question 9 A regular hexagon has a perimeter of 180 meters. How long is one side? (* Regular means that the sides are all the same length.) Answer 9	Question 10 The area of a rectangle is 28 square inches. The length is three more than the width. Find the dimensions of the rectangle. (* If you get this set up, you'll be doing well. You can't solve this unless you know the Quadratic Formula.) Answer 10

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Answer 1
let w = # of white stripes = 10
2w = # of blue stripes = 2(10) = 20
3w - 10 = # of gold stripes = 3(10) - 10 = 20

w + 2w + 3w - 10 = 50
6w = 60
w = 10

Back to question 1

Answer 2
let x = # in line for men's room = 13
2x = # in line for women's room = 2(13) = 26

x + 2x = 39
3x = 39
x = 13

Back to question 2

Answer 3
let p = price of 1 adult ticket = $5
1/3 p = price of 1 child's ticket

2p = price of 2 adult tickets
3(1/3p) = price of 3 kid's tickets

2p + 3(1/3p) = 15
2p + p = 15
3p = 15
p = 5

Back to question 3

Answer 4
let x = Alex's age now = 1
x+7 = Zach's age now = 1+7 = 8

x+5 = Alex's age in 5 yrs.
x+7+5 = x+12 = Zach's age in 5 yrs.

x+5 + x+12 = 19
2x + 17 = 19
2x = 2
x = 1

Back to question 4

Answer 5
let t = small pumpkin's weight
t +15 = medium pumpkin's weight
t + 15+15 = t +65 = large pumpkin's weight

3t = weight of 3 small pumpkins
3(t + 15) = weight of 3 medium pumpkins
3(t + 65) = weight of 3 large pumpkins

3t + 3(t + 15) + 3(t + 65) = 555
3t + 3t + 45 + 3t + 195 = 555
9t + 240 = 555
9t = 315
t = 35

t = 35
t + 15 = 35 + 15 = 50
t + 65 = 35 + 65 = 100

Back to question 5

Answer 6
let p = original price of 1 CD = $12.99

p - 5 = sale price of 1 CD

8(p-5) = 63.92
8p - 40 = 63.92
8p = 103.92
p = 12.99

Back to question 6

Answer 7
let t = time (in minutes) to mix ingredients = 7
2t + 1 = time (in minutes) to bake

t + 2t + 1 = 22
3t + 1 = 22
3t = 21
t = 7

Back to question 7

Answer 8
let w = time (in hours) to wash the truck = 1
w + 2 = time (in hours) to wax the truck

w + w+2 = 4
2w + 2 = 4
2 w = 2
w = 1

Back to question 8

Answer 9
let y = length of 1 side (in meters) = 30

6y = 180
y = 30

Back to question 9

Answer 10
let w = width (in inches)
w + 3 = length (in inches)

w ( w + 3 ) = 28
w² + 3w = 28

*remember, you can't solve this unless you know the Quadratic Formula

Back to question 10

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