# UNITARY METHOD DIRECT VARIATION

Unitary Method :

Unitary-method is all about finding value to a single unit.

Unitary-method can be used to calculate cost, measurements like liters and time.

Example :

If 30 pens cost \$45,

then  the cost of one pen is  =  45 / 30  =  \$1.50

Direct Variation :

If an increase in one quantity produces a proportionate  increase in another quantity, then the two quantities are directly proportional to each other

or

If a decrease in one quantity produces a proportionate  decrease in another quantity, then the two quantities are directly proportional to each other

Changes in both the quantities must be same.

That is,

Increase ------> Increase

or

Decrease ------> Decrease ## Solved Problems

Problem 1 :

Solution :

This is a situation of direct variation.

Because,

less number of basket balls -----> cost will be less

Given : 75 basketballs cost \$1,143.75

Cost of one basket ball is

=  1143.75 / 75

=  \$15.25

Then, the cost of 26 basket balls is

=  26  15.25

=  396.50

So, the cost of 26 basket balls is \$ 396.50

Problem 2 :

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

Solution :

This is a situation of direct variation.

Because,

more gallons of juice -----> amount received will be more

Given : 2 gallons of juice cost \$4

Cost of one gallon of juice is

=  4 / 2

=  \$2

Cost of 17 gallons of juice is

=  17  2

=  \$34

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

Problem 3 :

The cost of a taxi is \$40.50 for 15 miles. Find the cost for 20 miles.

Solution :

This is a situation of direct variation.

Because,

more miles -----> cost will be more

Given : Cost for 15 miles is \$40.50

Cost for one mile is

=  40.50 / 15

=  \$2.70

Then, the cost for 20 miles is

=  20 ⋅ 2.70

=  54

So, the cost for 20 miles is \$54.

Problem 4 :

In a business, if A can earn \$7500 in 2.5 years, At the same rate, find his earning for 4 years.

Solution :

This is a situation of direct variation.

Because,

more time  -----> more earning

Given : Earning for 2.5 years is \$7500

Earning for 1 year  is

=  7500 / 2.5

=  \$3000

Then, earning for 4 years is

=  4  3000

=  \$12000

So, the earning for 4 years is \$12000.

Problem 5 :

In 36.5 weeks, Miguel raised \$2,372.50 for cancer research. How much money will he raise in 20 weeks ?

Solution :

This is a situation of direct variation.

Because,

less number of weeks ----> amount raised will be less

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

Amount raised in one week is

=  2372.5 / 36.5

=  \$65

Amount raised in 20 weeks is

=  65  20

=  \$1300

So, the money raised in 20 weeks is \$1300.

Problem 6 :

Shanel gets 2/5 of a dollar for 1/7 hour of work.How much money does she get for 3 hours ?

Solution :

This is a situation of direct variation.

Because,

more hours -----> more earning

Pay for 1/7 hour of work  =  \$2/5

Pay for 1 hour of work is

=  (2/5) / (1/7)

=  (2/5)  (7/1)

=  14 / 5

=  \$2.8

Then, pay for 3 hours of work is

=  2.8  3

=  8.4

So, Shanel gets \$8.4 for 3 hours of work.

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 :

This is a situation of direct variation.

Because,

more gasoline  -----> more cost

Cost of 3/35 of a gallon  =  \$1/5

Cost of 1 gallon is

=  (1/5) / (3/35)

=  (1/5)  (35/3)

=  7 / 3

=  2.3

So, the cost of 1 gallon of gasoline is \$ 2.30.

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 :

This is a situation of direct variation.

Because,

more miles -----> more cost

Cost for one mile  =  \$2.25

Cost of 300 miles is

=  2.25  300

=  \$675

So, the total cost for the trip is \$675.

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 :

This is a situation of direct variation.

Because,

less units -----> less cost

Cost of 330 units  =  \$495

Cost of 1 unit is

=  495 / 330

=  1.5

Cost of 270 units is

=  1.5  270

=  \$405

So, John has to pay \$405 for 270 units.

Problem 10 :

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

Solution :

This is a situation of direct variation.

Because,

less hours -----> less earning

Given : Earning in 8 hours  =  \$ 416

Earning in 1 hour  =  \$ 52

Earning in 2.8 hours  =  52  2.8  =  145.6

So, Mr. David will earn \$145.6 in 2.8 hours. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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