Unit Rates & Better Buys — Challenge

Reduce everything to one of something, and comparisons become obvious.

What these problems cover

These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

Four pounds of coffee cost $12. What is the cost per pound in dollars?

  1. 2
  2. 3
  3. 4
  4. 6
  5. 48
Worked answer

3

A unit rate is the cost for one pound, so divide the cost by the number of pounds.

124 = 3 dollars per pound.

Problem 2

A car travels 240 miles on 8 gallons of fuel. How many miles does it travel per gallon?

  1. 24
  2. 28
  3. 30
  4. 32
  5. 36
Worked answer

30

Miles per gallon means miles divided by gallons.

2408 = 30 miles per gallon.

Problem 3

A reader finishes 15 pages in 3 minutes. At that rate, how many pages does the reader finish per minute?

  1. 3
  2. 4
  3. 5
  4. 6
  5. 45
Worked answer

5

Divide the pages by the minutes to get the rate for one minute.

153 = 5 pages per minute.

Problem 4

A driver covers 96 miles in 90 minutes. For the first 30 minutes the average speed was 60 miles per hour. What was the average speed in miles per hour for the remaining 60 minutes?

  1. 60
  2. 64
  3. 65
  4. 66
  5. 70
Worked answer

66

In the first 30 minutes, which is half an hour, the driver covered 60·12 = 30 miles.

That leaves 96-30 = 66 miles still to cover.

The remaining time is 60 minutes, exactly one hour, so the average speed over it is 66 miles per hour.

Problem 5

Six cans of soup cost $4.50. What does one can cost in dollars?

  1. 0.65
  2. 0.70
  3. 0.75
  4. 0.80
  5. 1.33
Worked answer

0.75

Divide the total cost by the number of cans.

4.506 = 0.75 dollars, or 75 cents, per can.

Problem 6

A 750 gram bag of oats costs $5.70. What is the cost in dollars per 100 grams?

  1. 0.72
  2. 0.74
  3. 0.76
  4. 0.78
  5. 0.80
Worked answer

0.76

There are 750100 = 7.5 hundred-gram portions in the bag.

5.707.5 = 0.76 dollars per 100 grams.

Problem 7

A dripping tap wastes 18 litres of water in 4 hours. How many litres does it waste per hour?

  1. 3.5
  2. 4
  3. 4.5
  4. 5
  5. 72
Worked answer

4.5

Divide the litres by the hours to get the rate for one hour.

184 = 4.5 litres per hour.

Problem 8

One and a half kilograms of rice cost $6. What is the cost in dollars per kilogram?

  1. 3
  2. 3.5
  3. 4
  4. 4.5
  5. 9
Worked answer

4

Divide the cost by the weight, even though the weight is not a whole number: 61.5.

61.5 = 4 dollars per kilogram.

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