SOLVING UNIT RATE WORD PROBLEMS

Problem 1 :

Sven drives his car 455 miles, using 14 gallons of gasoline. How many miles per gallon does his car get?

Solution :

Distance covered by Sven using

14 gallons of gasoline = 455 miles

To find the distance covered by his car using 1 gallon of gasoline, we will divide by 14 on both sides.

1 gallon of gasoline = 455/14

= 32.5 miles

So, he can cover 32.5 miles using 1 gallon of gasoline.

Problem 2 :

The grocery store charges $3.99 for a case of 24 bottles of water. What is the unit price?

Solution :

Cost of 24 bottles of water = $3.99

Cost of 1 bottle of water = 3.99/24

= 0.166

So, the unit price is $0.166.

Problem 3 :

The pressroom at a printing plant prints 540,000 sections in 12 hours. How many sections are printed per hour?

Solution :

Number of sections printed in 12 hours = 540, 000

Number of prints in 1 hour = 540, 000/12

= 45000

So, 45000 sections can be in 1 hour printed.

Problem 4 :

The bindery at a printing plant assembles 96,000 magazines in 12 hours. How many magazines are assembled in one hour?

Solution :

Number of magazines assembled in 12 hours = 96000

Number of magazines assembled in 1 hour = 96000/12

= 8000

So, 8000 magazines can be assembled in 1 hour.

Problem 5 :

The pet store has a special on cat food. The price is $4.32 for 12 cans. How much does each can cost?

Solution :

Cost of 12 cans of cat food = $4.32

Cost of 1 can = 4.32/12

= $0.36

So, cost of 1 can food is $0.36.

Problem 6 :

The grocery store has a special on macaroni and cheese. The price is $3.87 for 3 boxes. How much does each box cost?

Solution :

Cost of 3 boxes = $3.87

Cost of 1 box = 3.87/3

= $1.29

So, cost of 1 box is $1.29.

Problem 7 :

One elementary school in Ohio has 684 students and 45 teachers. Write the student-to-teacher ratio as a unit rate.

Solution :

Given :

45 teachers : 684 students

Dividing both parts by 45, we get

1 teacher : 684/45 students

1 teacher : 15.2

Approximately 15.

So, 1 teacher can teach 15 students.

Problem 8 :

A popular fast food burger weighs 7.5 ounces and contains 540 calories, 29 grams of fat, 43 grams of carbohydrates, and 25 grams of protein. Find the unit rate of 

a) calories per ounce

b)  grams of fat per ounce

c) grams of carbohydrates per ounce

d) grams of protein per ounce.

Round to two decimal places.

Solution :

a) 7.5 ounces : 540 calories

Dividing both parts by 7.5, we get

1 ounce : 540/7.5 calories

1 ounce : 72 calories

b) 7.5 ounces : 29 grams of fat

Dividing both parts by 7.5

1 ounce : 29/7.5

1 ounce : 3.86

c) 7.5 ounces : 43 grams of carbohydrates

Dividing both parts by 7.5, we get

1 : 43/7.5 grams of carbohydrates

1 ounce : 5.733 grams of carbohydrates

d) 7.5 ounce : 25 grams of protien

Dividing both parts by 7.5, we get

1 ounce : 25/7.5

1 ounce : 3.33 grams of protien

Problem 9 :

The graph shows the cost of buying tickets to a concert.

a. What does the point (4, 122) represent?

b. What is the unit rate?

c. What is the cost of buying 10 tickets?

Solution :

x-axis represents number of tickets.

y - axis represents the cost of tickets in dollars.

a. When number of tickets is 4, the cost of tickets will be $122.

b. Unit rate = 122/4

= 30.5

Cost of 1 ticket = $30.5

c. Cost of 10 tickets = 30.5 x 10

= $305

Problem 10 :

A sports store sells three different packs of tennis balls. Which pack is the best buy? Explain.

Solution :

Cos of 4 packs = $11.49

Cost of 1 pack = 11.49/4

= 2.8725

Cost of 6 packs = $16.79

Cost of 1 pack = 16.79/6

= $2.7983

Cost of 9 packs = $22.99

Cost of 1 pack = 22.99/9

= $2.5544

By comparing the unit rates, purchasing 9 packs of tennis balls is cheaper.

Problem 11 :

It costs $68 for 16 square feet of flooring. How much does it cost for 12 square feet of flooring?

Solution :

Cost of 16 square feet of flooring = $68

Cost of 1 square feet of flooring = 68/16

= $4.25

Cost of 12 square feet of flooring = 12 x 4.25

= $51

So, the required cost of 12 square feet is $51.

Problem 12 :

An oil spill spreads 25 square meters every 1/6 hour. How much area does the oil spill cover after 2 hours?

Solution :

To spread 25 square meter, we need 1/6 hour

Quantity of oil spread in 2 hours = 2 x 25 / (1/6)

= 2 x 25 x (6/1)

= 50 x 6

= 300 square feet

Problem 13 :

You mix 1/4 cup of juice concentrate for every 2 cups of water to make 18 cups of juice. How much juice concentrate and water do you use?

Solution :

2 cups = 1/4 cup of juice concentrate

1 cup = 1/8 cups of juice concentrate

18 cups = 18 x (1/8)

= 9/4

= 2  1/4 cups of juice concentrate