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You can click here and read the posting on **A family in Singapore** about Sarin’s family.

Read also the posting on **Sarin learns the concept of Fraction (mathematics concept)** to understand the concept of Fraction.

*Challenge yourself with the question before look for the given solution‼!*

**Upper primary school mathematics question UPQ321**

Sarin and Hairu had some money. Sarin’s money was $80 more than Hairu. After Sarin spent 1/4 of his money and Hairu spent 1/3 of his money, Sarin still had $83 more than Hairu. How much money did Hairu have at first?

Solution:

Sarin had $80 more than Hairu at first

The initial Math Model

Saroin spent 1/4 of his money and Hairu spent 1/3 of his money

Redraw the model by portion Sarin’s money to 4 equal portions and Hairu’s money to 3 equal portions

Subdivide the blue unit blocks to 4 × 3 = 12 equal units

After both of them spend the amount, Sarin still has $83 more than Hairu

The model can be rearrange with the amount spent included as shown

Per the model

1 unit + 60 = 83

1 unit = 83 – 60 = $23

The amount of money Hairu had at first = 12 × 23 = $276

Alternative Solution(1):

By equations,

Set S as money that Sarin had at first

Set H as money that Hairu had at first

Sarin had $80 more than Hairu at first

S = H + 80

After Spending, Sarin more than Hairu by $83

Sarin spent 1/4 fraction of his money and left with 3/4 fraction of money

Hairu spent 1/3 fraction of his money and left with 2/3 fraction of money

3/4 S = 2/3 H + 83

S = 8/9 H + 83 × 4/3

H + 80 = 8/9 H + 83 × 4/3

1/9 H = 83 × 4/3 – 80

H = 9 × 83 × 4/3 – 9 × 80 = $276

The amount of money Hairu had at first was $276

Alternative Solution(2):

Set H as Hairu’s money at first

Sarin’s money = H + 80

Sarin spent 1/4 fraction of his money

Sarin left = 3/4 fraction of his money = 3/4 × (H + 80)

Hairu spent 1/3 fraction of his money

Hairu left = 2/3 × H

After spending, Sarin had $83 more than Hairu

3/4 × (H + 80) – 2/3 × H = 83

3/4 H – 2/3 H = 83 – 3/4 × 80

1/12 H = 83 – 60 = 23

H = 12 × 23 = 276

The amount of money Hairu had at first = 12 × 23 = $276