UNITARY METHOD IN PERCENTAGE

John's doctor has told her she is obese, and needs to lose 10% of her body weight. This means she needs to lose 9 kg. How can we find out John’s current weight?

The Unitary Method can be used to solve this problem. We first find 1%, then multiply it by 100 to find the whole amount.

Example 1 :

Find 100% if 

a) 20% is 240 mL

b) 36% is 288 g

c) 7% is $126

Solution :

(a)  Let 100% of the quantity be x.

Given :

20% of x  =  240

(20/100) ⋅ x  = 240

x  =  240 ⋅ (100/20)

x  =  1200 ml

So, 100% of quantity is 1200 ml.

(b)  Let 100% of the quantity be x.

Given :

36% of x  =  288

(36/100) ⋅ x  = 288

x  =  288 ⋅ (100/36)

x  =  800

So, 100% of quantity is 800 g.

c) Let 100% of the quantity be x.

Given :

7% of x  =  126

(7/100) ⋅ x  = 126

x  =  126 ⋅ (100/7)

x  =  1800

Example 2 :

60% of a quantity if 15% of the quantity is 45.

Solution :

Let x be the quantity.

15% of x  =  45

1% of x  =  45/15

1% of x  =  3

60% of x  =  3(60)

60% of x  =  180

So, 60% of the required quantity is 180.

Example 3 :

36% of students at a school use public transport. If 144 students use public transport, how many students attend the school?

Solution :

Let x be the number of students in the school

Number of students who use public transport  =  144

36% of x  =  144

x  =  144  (100/36)

x  =  400

Example 4 :

An alloy contains 16% zinc and the rest is pure copper. If 20 kg of zinc is used to make the alloy, how much :

a) alloy is produced

b) copper is used?

Solution :

Let x be the quantity of alloy.

16% of x  =  20 kg

x  =  20 ⋅ (100/16)

x  =  125

So, quantity of alloy used is 125 kg.

100 - 16  ==>  84

Quantity of copper  =  84% of 125 

=  0.84 (125)

=  105 kg.

Example 5 :

John scored 60% for a test. If his actual score was 72, what was the maximum mark possible for the test?

Solution :

Let x be the maximum possible score.

60% of x  =  72

0.60x  =  72

x  =  72/0.60

x  =  120

So, the maximum possible score is 120.

Example 6 :

Suzanna’s doctor told her to lose 9 kg, which was 10% of her body weight.

a) How much did Suzanna weigh?

b) If Suzanna lost 12% of her body weight, what is her new weight

Solution :

Let x be the Suzanna's weight.

(a)  10% of x  =  9

x  =  9 ⋅ (100/10)

x  =  90 kg

(b)  12% of x  =  12/100 of 90

Weight she lost  =  10.8

Her new weight  =  90 - 10.8

=  79.2 kg

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