Unit Rates
If 5 apples cost $3, what is the unit rate (cost per apple)?
$0.60 per apple
Are the ratios 2 : 3 and 4 : 6 equivalent?
Yes
In the proportional relationship y = 5x, what is the constant of proportionality?
5
True or False: A proportional graph always passes through the origin.
True
If 8 pencils cost $2.40, how much do 12 pencils cost?
2.40/8 = 0.30; for 12 pencils: 12 x 0.30 = $3.60
Sarah runs 7.5 miles in 1.5 hours. What is her average speed in miles per hour?
7.5 divide 1.5 = 5 mph
Complete the proportion:
7 : 11 = ? : 22
14
7 : 11 = 14 : 22
In a table, when x = 4, y = 12; when x = 7, y =21. What is y = kx?
Since 12/4 = 3 and 21/7 = 3, k = 3, so y = 3x
A line passes through (2, 6). If it's proportional, what is the equation y = kx?
k = 6/2 = 3, so y = 3x
A mix of 4 parts water to 1 part juice concentrate uses 3 liters of concentrate. How many liters of water are needed?
If concentrate = 1 part = 3 L, then water = 4 parts = 4 x 3 = 12 L
A car travels 120 miles in 2 hours and 30 minutes. What is its rate in miles per hour?
120/2.5 = 48 mph
Which ratio is equivalent to 5 : 8?
a. 20 : 32
b. 9 : 14
c. 15 : 24
d. 25 : 39
a. 20 : 32
If y = kx and when x = 5, y = 17.5, find k.
k = 17.5/5 = 3.5
Given the graph with points (3, 12) and (5, 20), what is the constant of proportionality and equation?
k = 12/3 = 4 or 20/5 = 4. Equation is y = 4x
A map scale says 1 in. = 6 miles. On the map, two cities are 4.5 in. apart. How far are they in real life?
4.5 x 6 = 27 miles
A recipe uses 3/4 cup sugar for 1/2 cup flour. What is the unit rate (sugar per flour)?
(3/4) divide (1/2) = (3/2) or 1.5 cups sugar per 1 cup flour
True or False:
0.75 : 1 = 3 : 4
True
For y = 0.6x, what is y when x = 25?
y = 0.6 x 25 = 15
Graph these two points are (1, 2) and (3, 8), then answer the question: Does the graph of the relation below represent a proportional relationship?
No, because it doesn't go through (0, 0), so not purely proportional.
A T-shirt cost $20 and is discounted 25%. Then sales tax of 8% is added. What's the final price?
25% of 20 = 5, so 20 - 5 = $15 for the shirt.
Then, 8% of 15 = 1.20, 15 + 1.20 = 16.20
The shirt will cost $16.20
A worker produces 45 widgets in 2 hours and 45 minutes. What is their rate per hour (round to the nearest hundredths)?
2 hours 45 minutes = 2.75 hr
45 divide 2.75 approx 16.36 widgets per hour
If a : b = 9 : 14, what is b : a ?
14 : 9
In a proportional scenario, if y = 4x + c, and you know it is proportional, what must c be?
c = 0, because a proportional relation must go through origin.
Graph the relation defined by y = 2/5x. What is y when x = 25?
(2/5) x 25 = 10 and the graph is a line through the origin with slope 2/5.
A recipe calls for 2/3 cup milk per 5 pancakes. How much milk for 12 pancakes?
(2/3) divide 5 = 2/15 cup per pancake.
For 12 pancakes: 12 x (2/15) = 24/15 = 1 3/5 cups.