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The story on Sarin’s family attend concert at the Esplanade you can read postings on **Sarin’s family attend concert at the Esplanade** in Welcome category and **Sarin’s family attend concert at the Esplanade Part 2 (Math Question)****.**

Click and read the posting on **Sarin learns the concept of Fraction (mathematics concept)** to understand Portion or Fraction.

You should read also the posting on **Sarin learns concept of ratio in school** to understand mathematics concept of Ratio.

Read the posting on **Sarin learns Symbol, Algebra and Equation in school (Math Concept) **to understand the concept of Algebra.

**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?

Solution:

Draw the model

From the model,

4N = 144 – 88 = 56

1N = 14

The number of novels on the shelf at first = 5 × 14 = 70

Alternative Solution(1):

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

Alternative Solution(2):

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