# COMPARING UNIT RATE WORD PROBLEMS

What is unit rate ?

The cost of 1 unit of product is known as unit price.

In this topic, we will compare prices of two or more types and decide which is the better deal.

To compare two or more types, we will find the unit rate. Then comparison can be done easily.

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

Problem 1 :

Mouthwash, 50.7-ounce size for \$6.99 or 33.8-ounce size for \$4.79.

Solution :

Let A and B two type’s pack of mouthwash

Type A : 50.7 ounce

Type B : 33.8 ounce

Cost of 1 ounce of type A mouth wash :

= 6.99 / 50.7

= \$0.137

Cost of 1 ounce of type B mouth wash :

= 4.79 / 33.8

= \$0.141

So, type A is better than type B.

Problem 2 :

Toothpaste, 6 ounce size for \$3.19 or 7.8-ounce size for \$5.19

Solution :

A and B two type’s pack of toothpaste

Type A : 6 ounce pack

Type B : 7.8 ounce pack

Cost of 1 ounce of type A tooth paste :

= 3.19 / 6

= \$0.531

Cost of 1 ounce of type B tooth paste :

= 5.19 / 7.8

= \$0.665

0.531 < 0.665

So, type A is better than type B.

Problem 3 :

Breakfast Cereal, 18 ounce for \$3.99 or 14 ounce for \$3.29

Solution :

A and B two types of breakfast cereal

Type A: 18 ounce

Type B: 14 ounce

Cost of 1 ounce of type A breakfast cereal :

= 3.99 / 18

= \$0.221

Cost of 1 ounce of type B breakfast cereal :

= 3.29 / 14

= \$0.235

So, type A is better than type B.

Problem 4 :

Breakfast Cereal, 10.7 ounce size for \$2.69 or 14.8-ounce size for \$3.69

Solution :

A and B two types of breakfast cereal

Type A : 10.7 ounce

Type B : 14.8 ounce

Cost of 1 ounce of type A breakfast cereal :

= 2.69 / 10.7

= \$0.251

Cost of 1 ounce of type B breakfast cereal :

= 3.69 / 14.8

= \$0.249

So, type B is better than type A.

Problem 5 :

Ketchup, 40-ounce regular bottle for \$2.99 or 64-ounce squeeze bottle for \$4.39

Solution :

A and B two types of ketchup bottle

Type A: 40 ounce

Type B: 64 ounce

Cost of 1 ounce of type A ketchup bottle :

= 2.99 / 40

= \$0.074

Cost of 1 ounce of type B ketchup bottle :

= 4.39 / 64

= \$0.068

So, type B is better than type A.

Problem 6 :

Mayonnaise 15-ounce regular bottle for \$3.49 or 22-ounce squeeze bottle for \$4.99

Solution:

A and B two types of mayonnaise bottle

Type A : 15 ounce

Type B : 22 ounce

Cost of 1 ounce of type A mayonnaise bottle :

= 3.49 / 15

= \$0.232

Cost of 1 ounce of type B mayonnaise bottle :

= 4.99 / 22

= \$0.226

So, type B is better than type A.

Problem 7 :

Cheese \$6.49 for 1 lb. block or \$3.39 for 1/2 lb. block

Solution :

A and B two types of cheese

Type A: 1 lb. block

Type B: 1/2 lb. block

Cost of 1 lb block = \$6.49 lb/block

Cost of 1/2 lb block = \$3.39

Multiplying by 2 on both sides, we get

Cost of 1/2 lb block = 2(3.39)

= \$6.78 lb/block

So, type A is better than type B.

Problem 8 :

Candy \$10.99 for a 1 lb. bag or \$2.89 for 1/4 lb. of loose candy

Solution :

A and B two types of candy

Type A: 1 lb.bag

Type B: 1/4 lb bag

Cost of 1 lb. bag of Type A = \$10.99 lb/bag

Cost of 1/4 lb bag = \$2.89

Multiplying by 4 on both sides, we get

Cost of 1 lb. bag of Type B = 2.89(4)

= \$11.56 lb/bag

So, type A is better than type B.

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