COMPARING UNIT RATE WORD PROBLEMS

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.

Problem 9 :

In whole milk, 13 parts out of 400 are milk fat. In 2% milk, 1 part out of 50 is milk fat. Which type of milk has more milk fat per cup?

Solution :

Whole milk is 100% of milk.

In 100% of milk,

quantity of milk fat = 13/400

Converting into percentage = (13/400) x 100%

= 3.25%

In 2% of milk, 

quantity of fat = 1/50

Converting into percetage = (1/50) x 100% 

= 2%

3.25% > 2%

Then in whole milk we have more fat.

Problem 10 :

A horse’s heart beats 440 times in 10 minutes. A cow’s heart beats 390 times in 6 minutes. Which animal has a greater heart rate?

Solution :

Unit rate of horse heart beat = 440/10

= 44 times per minute

Unit rate of cow's heart beat = 390/6

= 40 times per minute

Comparing the unit rates, horse has greater heart beat.

Problem 11 :

Three album downloads cost $36. How much do 5 album downloads cost?

Solution :

Cost of downloading 3 albums = $36

Cost of downloading 1 album = 36/3

= 12

Cost of downloading 5 albums = 5(12)

= $60

Problem 12 :

You can buy 20 fluid ounces of shampoo for $4.40 or 24 fluid ounces for $4.80. Which is the better buy? Explain.

Solution :

Unit price of 20 fluid ounce of shampoo = 4.40/20

= 0.22

Unit price of 24 fluid ounce of shampoo = 4.80/24

= 0.2

Comparing the unit rates, buying 24 fluid ounces pack is better.