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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