The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presenting the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids will able to acquire knowledge of dealing with the Math Modeling, the Math Problem Solving and the Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Algebra, Ratio, Fraction and Problem Sum.

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

Read the posting on **Sarin learns concept of ratio in school**** **to understand the concept of Ratio.

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 Symbol, Algebra and Equation in school (Math Concept)**** **to understand the concept of Algebra.

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

**Upper primary school mathematics question UPQ421**

Sarin, Hairu and Fatimah received a sum of money from their father. Sarin received ¼ of the total sum received by Hairu and Fatimah. Hairu received 1/9 of the total sum received by Sarin and Fatimah. Father gave Fatimah $60 more than Hairu. How much did their father given to them?

Solution:

Solve by using Fraction model

First to draw the fraction (1/9) that Hairu received

Add in the information on the fraction (1/4) that Sarin received

Fatimah received $60 more than Hairu

Per the model

6 units = 60

1 unit = $10

The amount given by their father = 10 × 10 = $100

Alternative Solution(1):

Using ratio,

Sarin received ¼ of the fraction of what Hairu and Fatimah recieved

Sarin : Hairu + Fatimah : Sarin + Hairu + Fatimah = 1 : 4 : 5 = 2 : 8 : 10

Hairu received 1/9 of the fraction of what Sarin and Fatimah recieved

Hairu : Sarin + Fatimah : Sarin + Hairu + Fatimah = 1 : 9 : 10

The amount given by their father is constant in both cases

Sarin : Hairu : Sarin + Hairu + Fatimah = 2 : 1 : 10

Sarin : Hairu : Sarin : Sarin + Hairu + Fatimah = 2 : 1 : 7 : 10

Fatimah had $60 more than Hairu from their father

6 units = 60

1 unit = $10

The amount given by their father = 10 × 10 = $100

Alternative Solution(2):

Using algebra and equation

Set S as the amount received by Sarin

Set H as the amount received by Hairu

Set F as the amount received by Sarin

The amount Sarin received equal to ¼ fraction of bothHairu and Fatimah received

4S = H + F

The amount Hairu received equal to 1/9 of both Sarin and Fatimah received

9H = S + F

S = 9H – F

4S = 36H – 4F

Therefore

H + F = 36H – 4F

35H = 5F

7H = F

Given also that Fatimah received $60 more than Hairu

H + 60 = F

Hence

7H = H + 60

6H = 60

H = 10

F = 7 × 10 = 70

S = 9 × 10 – 70 = 20

The amount given by their father = H + F + S = 10 + 20 + 70 = $100

hi, I have seen your solution but I don’t quite understand as you drew 10 units instead of 9 units to represent Sarin and Fatimah. I have a similar question that I couldnt solve thus am hoping you could help me with me:

Andy, Bala, Candice and David each donated some money to charity. andy’s donation was 1/5 of the total donation made by Bala,Candice and David. Bala’s donation was 2/7 of the total donation made by Andy, Candice and David. Candice’s donation was 1/4 of the total donation made by Andy, Bala and David. David donated $42.75 more than Candice. How much did they donate altogether?

Hi Pam,

Thanks for pointing out the error in the model. The amount that Sarin has should be 2 units instead of 3. I must have overlook it when transfer in to the drawing board. The work out is based on 10 units which is correct and answer is accurate. I updated the model.

For your question, it is best to use the Alternative solution (1) the ratio method to solve it.

they is no change in total amount. Based on the given 3 conditions, you will be able to work out the ratio of Andy(A), Bala(B), Candice(C) and David(D). Since David donated $42.75 more than Candice, you can work out the total amount.

A : B : C : D : All = 15 : 20 : 18 : 37 : 90 ==> 1 unit = $2.25

The total amount = $202.50

Email to me (kcboh01@yahoo.com.sg) if you can not get the answer.

I purchase the new office 2013 software but facing problem in downloading and installing. I lost my old copy of office software. I will sent you a detail workout using ratio method if I can get the new office software work.

Please wish me good luck!!