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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