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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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

Let us look at the next problem on "Unit price word problems"

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 

Let us look at the next problem on "Unit price word problems"

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 $120

Cost of 1 doll  =  120 / 8

Cost of 1 doll  =  $15

6 dolls cost $102

Cost of 1 doll  =  102 / 6

Cost 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

Let us look at the next word problem on "Unit price"

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  =  $4

Cost of 1 pencil  =  4 / 10

Cost of 1 pencil  =  $0.40

Cost of 6 pencils  =  $2.70

Cost of 1 pencil  =  2.7 / 6

Cost 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

Let us look at the next problem on "Unit price word problems"

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 $3.80

Cost of 1 liter  =  3.8 / 2

Cost of 1 liter  =  $ 1.90

2 liters of milk at $2.70

Cost of 1 liter  =  2.7 / 1.5

Cost 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

Let us look at the next word problems on "Unit price"

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. 

David

Earning in 8 hrs  =  $57.60

Earning in 1 hr  =  57.60 / 8

Earning in 1 hr  =  $7.20

John

Earning in 12 hrs = $90

Earning in 1 hr  =  90 / 12

Earning in 1 hr  =  $7.50

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

Hence, John is earning better

Let us look at the next word problem on "Unit price"

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 -----> $3.25

1 kilogram  =  2 x 500 grams 

Price of 1 kg  =  2 x 3.25

Price of 1 kg  =  $6.5

1.5 kilograms -----> $9.9

Price of 1 kg  =  9.9 / 1.5

Price 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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