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

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

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

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

**Upper primary school mathematics question UPQ516**

Sarin and Hairu had given a sum as their allowance monthly by their mother. Sarin’s monthly allowance is $42 more than Hairu’s. Hairu spends $54 more than Sarin every month. Hairu’s savings is ½ of Sarin’s savings. If Sarin spends 3/7 of his allowance every month, what is his allowance for the entire year?

Solution:

Sarin’s spends 3/7 of his allowance monthly,

The model for monthly allowance

Per the model,

2 units = 54 + 42 = 96

1 unit = 48

Sarin’s monthly allowance = 7 × 48 = 336

Sarin’s allowance for a year = 12 × 336 = $4032

Alternative solution(1):

Express using ratio,

For Sarin,

SSaving : Sspend : Sallowance = 4 : 3 : 7 = 4U : 3U : 7U

For Hairu,

Saving is half and spending is $54 more

HSaving : Hspend : Hallowance = 4U × ½ : 3U + 54 : 2U + 3U + 54 = 2U : (3U + 54) : (5U + 54)

Since, Sarin allowance is $42 more than Hairu

7U = 5U + 54 + 42 = 5U + 96

2U = 96

1U = $48

Sarin’s allowance monthly = 7 × 48 = $336

Sarin’s allowance for a year = 12 × 336 = $4032

Alternative Solution(2):

Express using fraction,

3/7 of Sarin’s allowance ==> Spending

4/7 of Sarin’s allowance ==> Saving

Hairu’s allowance + $42 ==> Sarin’s allowance

Hairu’s saving ==> 2/7 of Sarin’s allowance

Hairu’s spending ==> 3/7 of Sarin’s allowance + $54

Hairu’s allowance ==> 5/7 of Sarin’s allowance + $54

Sarin’s allowance ==> 5/7 of Sarin’s allowance + $54 + $42

2/7 of Sarin’s allowance ==> $96

2 units = $96

1 unit = $48

Sarin’s allowance ==> 7 × 48 = $336

Sarin’s allowance for a year è 12 × 336 = $4032