**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 **

**Problem 1 :**

75 basketballs cost $1,143.75. Find the cost of 26 basketballs

**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.

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