# Fatimah and Hairu enjoy Congkak game part 30 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can aquire the skills 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 AlgebraRatio and Problem Sum.

Read the posting on Fatimah and Hairu play Congkak to know about Congkak game.

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

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

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

Upper primary school mathematics question UPQ507

After a congkak game, Hairu and Fatimah each has a certain number of marbles. If Fatimah gives Hairu 40 marbles, Hairu will have twice as many marbles as Fatimah. If Hairu gives Fatimah 40 marbles, Fatimah will have thrice as many marbles as Hairu. How many more marbles does Fatimah have than Hairu?

Solution:

In both cases, the total number of marbles did not change

The final ratio,

Case 1 Hairu : Fatimah : Total = 2 : 1 : 3 = 8 : 4 : 12

Case 2 Hairu : Fatimah : Total = 1 : 3 : 4 = 3 : 9 : 12

In case 1, Faimah gives Hairu 40 marbles

In case 2, Fatimah receives 40 marbles from Hairu

Per the model,

5 units = 80

1 unit = 16

The number of marbles Fatimah has = 4 × 16 + 40 = 104

The number of marbles Hairu has = 3 × 16 + 40 = 88

The number of marble Fatimah more than Hairu = 104 – 88 = 16

Alternative solution:

Using algebra expression

Set F as the number of marbles Fatimah has

Set H as the number of marbles Hairu has

When Fatimah gives 40 marbles to Hairu, Hairu has twice number of marbles than Fatimah

Therefore,

2 × (F – 40) = H + 40

2F – 80 = H + 40

H = 2F – 120

When Hairu gives 40 marbles to Fatimah, Fatimah has three time marbles than Hairu

Hence,

F + 40 = 3 × (H – 40)

F + 40 = 3H – 120

F = 3H – 160

Since H = 2F – 120

F = 3 × (2F – 120) – 160

F = 6F – 360 – 160

5F = 520

F = 104

H = 2 × 104 – 120 = 88

The number of marbles Fatimah more than Hairu = F – H = 104 – 88 = 16