# UNIT PRICE WORD PROBLEMS

## About "Unit price word problems"

"Unit price word problems" is a much required stuff for the kids who study math in math in primary level.

Before we look at unit price word problems, let us look at some basic stuff about unit price.

Unit price definition and example :

Definition :

Unit price is nothing but the cost or price of one unit of a product or service.

Example :

If 18 units of a product cost \$360,

then  price per unit is  = 360 / 18  =  \$20

## Unit price word problems

To have better understanding unit price, let us look at some unit price word problems

Problem 1 :

75 basketballs cost \$1,143.75. Find the unit rate in price per basketball.

Solution :

Given : 75 basketballs cost \$1,143.75

Then, price pf one basket ball  =  1143.75 / 75  =  15.25

Hence, the unit rate in price per basket ball is \$ 15.25

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Problem 2 :

If David sells 2 gallons of juice for \$4, how much money will he earn by selling 17 gallons of juice ?

Solution :

Given : 2 gallons cost \$4

Then, the price pf one gallon  =  4 / 2  =  \$2

Price of 17 gallons  =  2 x 17  =  \$34

Hence, David will earn \$34 by selling 17 gallons of juice

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Problem 3 :

The cost of a taxi is \$40.50 for 15 miles. Find the cost per mile.

Solution :

Cost for 15 miles  =  40.50

Cost for one mile  =  40.50 / 15  =  2.70

Hence, the cost per mile is \$2.70

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Problem 4 :

In a business, if A can earn \$ 7500 in 2.5 years, find the unit rate of his earning per month.

Solution :

Given : Earning in 2.5 years  =  \$ 7500

1 year  =  12 months

2.5 years  =  2.5 x 12  =  30 months

Then, earning in 30 months  =  \$ 7500

Therefore, earning in 1 month  =  7500 / 30  =  \$ 250

Hence, the unit rate of his earning per month is \$ 250

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Problem 5 :

In 36.5 weeks, Miguel raised \$2,372.50 for cancer research. How was his unit rate in price per week?

Solution :

Given : Miguel raised \$2, 372.50 in 36.5 weeks

Then, amount raised in one week  =  2372.5 / 36.5  =  65

Hence, the unit rate in price per week was \$ 65

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Problem 6 :

Shanel gets 2/ 5 of a dollar for 1/7 hour of work.How much money does she get per hour ?

Solution :

Pay for 1/7 hour of work  =  \$2/5

Pay for 1 hour of work  =  (2/5) / (1/7)

Pay for 1 hour of work  =  (2/5) x (7/1)

Pay for 1 hour of work  =  14 / 5

Pay for 1 hour of work  =  \$2.8

Hence, Shanel gets \$2.8 per hour

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Problem 7 :

If 3 /35 of a gallon of gasoline costs 1/5 of a dollar, find the price of 1 gallon of gasoline.

Solution :

Cost of 3/35 of a gallon  =  \$1/5

Cost of 1 gallon  =  (1/5) / (3/35)

Cost of 1 gallon  =  (1/5) x (35/3)

Cost of 1 gallon  =  7 / 3

Cost of 1 gallon  =  2.3

Hence, the cots of 1 gallon of gasoline is \$ 2.30

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Problem 8 :

Declan would like to hire a call taxi for 300 miles trip. If the cost of the taxi is \$2.25 per mile, what is the total cost for his  trip ?

Solution :

Cost for one mile  =  \$2.25

Cost for 300 miles  =  2.25 x 300

Cost for 300 miles  =  \$675

Hence, the total cost for the trip is \$675

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Problem 9 :

John ordered 330 units of a product for \$495. Then he reduced his order to 270 units. How much money does John have to pay for 270 units ?

Solution :

Cost of 330 units  =  \$495

Cost of 1 unit  =  495 / 330

Cost of 1 unit  =  1.5

Cost of 270 units  =  1.5 x 270

Cost of 270 units  =  \$405

Hence, John has to pay \$405 for 270 units

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Problem 10 :

My David earns \$416 in 8 hours. How much does earn in 2.8 hours ?

Solution :

Given : Earning in 8 hours  =  \$ 416

Earning in 1 hour  =  \$ 52

Earning in 2.8 hours  =  52 x 2.8  =  145.6

Hence, Mr. David will earn \$145.6 in 2.8 hours

## Comparing unit prices

Problem 1 :

Which is the best deal,

8 dolls cost \$120

or

6 dolls cost \$102 ?

Solution :

To compare the given measures, convert them in to unit rates.

 8 dolls cost \$120Cost of 1 doll  =  120 / 8Cost of 1 doll  =  \$15 6 dolls cost \$102Cost of 1 doll  =  102 / 6Cost of 1 doll  =  \$17

We get the lowest price per doll is \$15 in "8 dolls cost \$120"

Hence, "8 dolls cost \$120" is the best deal

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Problem 2 :

Which is the best deal,

10 pencils cost \$4

or

6 pencils cost \$2.70 ?

Solution :

To compare the given measures, convert them in to unit rates.

 Cost of 10 pencils  =  \$4Cost of 1 pencil  =  4 / 10Cost of 1 pencil  =  \$0.40 Cost of 6 pencils  =  \$2.70Cost of 1 pencil  =  2.7 / 6Cost of 1 pencil  =  \$0.45

We get the lowest price per pencil \$0.40 in "10 pencils cost \$4"

Hence, "10 pencils cost \$4" is the best deal

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Problem 3 :

Which is the best deal,

2 liters of milk at \$3.80

or

1.5 liters of milk at \$2.70 ?

Solution :

To compare the given measures, convert them in to unit rates.

 2 liters of milk at \$3.80Cost of 1 liter  =  3.8 / 2Cost of 1 liter  =  \$ 1.90 2 liters of milk at \$2.70Cost of 1 liter  =  2.7 / 1.5Cost of 1 liter  =  \$ 1.8

From the above unit rates, we get the lower price per liter of milk \$1.8 in "2 liters cost \$2.70"

Hence, "2 liters cost \$2.70" is the best deal

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Problem 4 :

Who is better in earning,

David earns \$57.60 in 8 hours

or

John earns \$90 in 12 hours ?

Solution :

To compare the given measures, convert them in to unit rates.

 DavidEarning in 8 hrs  =  \$57.60Earning in 1 hr  =  57.60 / 8Earning in 1 hr  =  \$7.20 JohnEarning in 12 hrs = \$90Earning in 1 hr  =  90 / 12Earning in 1 hr  =  \$7.50

From the above unit rates, John earns more than David per hour.

Hence, John is earning better

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Problem 5 :

Which is best,

500 grams cheese cost \$ 3.25

or

1.5 kilograms cheese cost \$ 9.9

Solution :

To compare the given measures, convert them in to unit rates in price per kilogram.

 500 grams -----> \$3.251 kilogram  =  2 x 500 grams Price of 1 kg  =  2 x 3.25Price of 1 kg  =  \$6.5 1.5 kilograms -----> \$9.9Price of 1 kg  =  9.9 / 1.5Price of 1 kg  =  \$6.6

From the above unit rates, we get the lower price per kilogram \$6.5 in "500 grams cheese cost \$ 3.25"

Hence, "500 grams cheese cost \$ 3.25" is the best deal

We hope that the students would have understood the stuff given on "Unit price word problems"

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