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You should read also the posting on Sarin learns concept of ratio in school to understand mathematics concept of Ratio.
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Upper primary school mathematics question UPQ503
There were 160 novels and comics on a shelf of the Esplande Library. When 2/5 of the novels and 2/3 of the comics were borrowed by the library users, the total number of novels and comics left on the shelf became 72. How many novels were there on the shelf at first?
Draw the model
From the model,
4N = 144 – 88 = 56
1N = 14
The number of novels on the shelf at first = 5 × 14 = 70
Using Algebra expression
Set N as number of novels on the shelf at first
Set C as number of comics on the shelf at first
The total number of books = N + C
The number of books borrowed = 2/5 N + 2/3 C
The number of books left = 3/5 N + 1/3 C
N + C = 160
C = 160 – N
3/5 N + 1/3 C = 72
9/15 N + 5/15 C = 72
9N + 5C = 15 × 72 = 1080
9N + 5 × (160 – N) = 1080
9N – 5N = 1080 – 800
4N = 280
N = 70
Thr number of novels on the shelf at first = 70
The ratio of the number of novels left on the shelf to the number of novels borrowed
N(Left) : N(borrowed) : Total novels = 3 : 2 : 5 = 3U : 2U : 5U
The ratio of number of comics left on the shelf to the number of comics borrowed
C(Left) : C(borrowed) : Total Comics = 1 : 2 : 3 = 1P : 2P : 3P
The number of books initially = 160
The number of books left = 72
The number of books borrowed = 160 – 72 = 88
2U + 2P = 88 ==> 1U + 1P = 44
3U + 1P = 72
2U = 72 – 44 = 28
1U = 14
The total number of novels on the shelf at first = 5 × 14 = 70