# Fatimah and Hairu enjoy Congkak game part 29 (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 PercentageFraction, Ratio and Problem Sum.

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

Read the posting on Sarin learns Average Number, Percentage and Charting in school (Math Concept) to know about Percentage.

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

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 UPQ490

Fatimah and Hairu played a CongKak game using. At first, 25% of the number of marbles that Fatimah had was 1/3 of the number of marbles that Hairu had. In the first round, Fatimah lost 65 of her marbles to Hairu. In the second round, Hairu lost 30 of his marbles to Fatimah. After the game, they had the same number of marbles.

(a) How many marbles did Fatimah have at first?

(b) How many marbles did Hairu have in the end?

Solution:

In the 2 rounds of the CongKak game, the number of stickers Fatimah lost = 65 – 30 = 35

The total number of marbles had not changed

25% = 25/100 = 1/4 of Fatimah’s marbles ==> 1/3 of Hairu’s marbles

The initial marbles ratio

Fatimah’s marbles : Hairu’s marbles : Total = 4 : 3 : 7 = 8 : 6 : 14

The final marbles ratio

Fatimah’s marbles : Hairu’s marbles : Total = 1 : 1 : 2 = 7 : 7 : 14

1 unit = 35 marbles

The number of marbles Fatimah has at first = 8 × 35 = 280

The number of marbles Hairu has at the end = 7 × 35 = 245

Alternative solution:

¼ of Fatimah’s marbles is equal to 1/3 of Hairu’s marbles

The model Finally, they have the same amount of marbles

The final number of marbles Fatimah lost to Hairu = 65 – 30 = 35

From the model,

1 unit = 35 marbles

Hence,

The number of marbles Fatimah has at first = 8 × 35 = 280

The number of marbles Hairu has at the end = 7 × 35 = 245