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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?
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
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
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
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