Unit Rates/Understanding Proportions
A tennis match was delayed because of rain. The officials were not prepared for the delay. They covered the 25ft by 20ft court with 13ft by 10ft plastic covers. How many plastic covers were needed to cover the court from the rain.
4 plastic covers
25 x 20 = 500
13 x 10 = 130
500 divided by 130 = 3.84
so 4 plastic covers
According to the information below, how much does one ticket cost?
3 tickets cost $21.00
4 tickets cost $28.00
5 tickets cost $35.00
6 tickets cost $42.00
1 ticket cost $7.00
21.00 divided by 3
28.00 divided by 4
35.00 divided by 5
42.00 divided by 6
3 hats cost a total of $18. Which equation describes the total cost, C, in terms of the number of hats, n?
a) C = 3n
b) C = 6n
c) C = 0.5n
d) 3C = n
b) C = 6n
$18 divided by 3 = $6 per hat
What value of "x" will make these two expressions equivalent?
-3/7 and x/21
-9
-3/7 = x/21
7x = -63
x = -9
Which of the following numbers is divisible by 3?
a) 459,732
b) 129,682
c) 1,999,000
d) 5,684,722
a) 459,732
459,732 divided by 3 = 153,244
One third of a quart of paint covers one fourth of a basketball court. How much paint does take to paint the entire basketball court?
1 1/3 quarts
1/3 x 4 = 4/3 = 1 1/3
1/4th of a basketball court can be covered by 1/3rd of a quart of paint then to cover the entire court 4 times the amount is required.
If y = 3x what is the constant of proportionality between y and x?
3
The cost to rent an apartment is proportional to the number of square feet in the apartment. An 800 square foot apartment costs $600 per month. What equation represents the relationship between area, a, and cost, C?
a) C = 0.75a
b) C = 1.33a
c) C = 8a
d) C = 6a
a) C = 0.75a
$600 divided by 800 = 0.75
Which of the expressions equals 60%. There can be more than 1 correct answer, select all the correct answers.
a) 48 of 100
b) 32.4 of 54
c) 3 of 5
d) 4 of 5
e) 32 of 53
b) 32.4 of 54
c) 3 of 5
32.4 divided by 54 = .60
3 divided by 5 = .60
Jared hiked a trail that is 12 miles long. He hiked the trail in section that were 1.5 miles each. In how many sections did he complete the hike?
8
12 miles divided by 1.5 miles = 8
What is the unit rate for a pound of seed? If
10 pounds cost $17.50
20 pounds cost $35.00
30 pounds cost $52.50
40 pounds cost $70.00
$1.75
17.50 divided by 10 = 1.75
35.00 divided by 20 = 1.75
52.50 divided by 30 = 1.75
70.00 divided by 40 = 1.75
When Frank buys three packs of pens, he knows he has 36 pens. When he buys five packs, he knows he has 60 pens. What is the constant of proportionality between the number of packs and the number of pens?
12
36 pens divided by 3 packs
60 pens divided by 5 packs
Sally paid $3.50 for 7 apples. Write an equation to represent the total cost "y" of buying "x" apples.
Select the correct equation to describe the situation. There may be more than one correct answer.
a) y = 7x b) 3.50y = x
c) y = 0.50x d) x = 7
e) y = 3.50x f) y = 3.50/7x
c) y = 0.50x
f) y = 3.50/7x
$3.50 divided by 7 apples = .50 per apple
At one particular store, the sale price, "s", is always 75% of the displayed price, "d". Which of the following equations correctly shows how to calculate "s" from "d"?
a) d = 75s
b) s = 0.75d
c) s = d - 0.75
d) s = d + 75
b) s = 0.75d
The equation should show the constant of proportionality
If the measure of the first of two complementary angles is 68 degrees, what is the measure of the second angle?
22 degrees
complementary angles add up to 90 degrees
90 - 68 = 22 degrees
Which of the following pairs of ratios form a proportion?
a) 9 boys to 5 girls and 12 boys to 8 girls
b) 9 boys to 5 girls and 18 boys to 10 girls
c) 9 boys to 5 girls and 13 boys to 9 girls
d) 9 boys to 5 girls and 27 boys to 14 girls
b) 9 boys to 5 girls and 18 boys to 10 girls
9/5 = 18/10
Suppose the relationship between x and y is proportional. If the constant of proportionality of y to x is 16, select possible values for y and x.
a) x = 6 and y = 96
b) x = 96 and y= 6
c) x = 9 and y = 90
d) x = 144 and y = 9
a) x = 6 and y = 96
To find constant of proportionality use
"y divided by x"
96 divided by 6 = 16
You run 9.1 miles in 1.3 hours at a steady rate. Write an equation that represents the proportional relationship between the "x" hours you run and the distance "y" in miles that you travel?
y = 7x
9.1 miles divided by 1.3 hours = 7 miles per hour
Jim is shopping for a suit to wear to his friend's wedding. He finds the perfect one on sake at 30% off. If the original price was $250.00, what will the selling price be after the discount?
$175
70/100 = x/250
100x = 17500
x = 175
or .70 x 250 = 175
Nelly spent 7/8 of his savings on furniture and the rest on a lawnmower. If the lawnmower cost him $250, how much did he spend on furniture?
$1750
8/8 - 7/8 = 1/8 on lawnmower
1/8s = 250
s = 2000
7/8 x 2000 = 1750
Ricky's family wants to invite his classroom to a "get acquainted" party. If 20 students attend the party then it will cost $100. Assuming the relationship between cost and guests is proportional, which of the following will be the cost if 29 students attend?
$145
20/100 = 29/x
20x = 2900
x = 145
When Georgia buys 3 boxes of peaches, she has 40 pounds more than when she buys 1 box of peaches. How many pounds of peaches are in each box?
20
3 boxes - 1 box = 2 boxes
Difference in the pounds is 40 pounds
40 divided by 2 is 20 pounds per box
Use the data in the table to give an equation to represent the proportional relationship.
x: y:
0.5 7
1 14
1.5 21
2 28
y = 14x
If Julie brought her prom dress on sale at 15% off and paid $110.49 before tax, find the original price of her dress.
$129.99
85/100 = 110.49/x
85x = 11049
x = 129.988 which is 129.99
Jim is 4 years older than his brother Bob. In two years, Jim will be twice Bob's age. How old are they now?
Bob is 2 and Jim is 6
Bob's age is "x" and Jim's age is "x + 4"
In 2 years Bob's age is " x + 2" and Jim's age is "x + 4 + 2"
In 2 years Jim's age is twice Bob's age
x + 6 = 2(x + 2)
x + 6 = 2x + 4