Fatimah and Hairu enjoy Congkak game part 10 (Math Question)

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

You can click and read postings  Sarin learns the concept of Fraction (mathematics concept) to understand concept of Fraction.

Upper primary school mathematics question UPQ85

Fatimah had a set of marbles used for the Congkak game. There were 120 green marbles & red marbles. 4/9 of the green marbles and 5/7 of the red marbles were big size. The rest of the 44 green marbles and red marbles were small size. How many green marbles were big size?

 Solution:

            We can set up a model by portion the marbles per the fraction of their size.

From the above model,

Total there were 120 marbles,

            9G + 7R = 120 ===> 18G + 14R = 240

            Total there are 44 small size marbles,

            5G + 2R = 44 ===> 35G + 14R = 308

            Solve the above equations,

            17G = 68

            G = 4 ===> one unit of green marbles

            Number of big size green marbles = 4 x 4 = 16

 Alternative solution:

            Assume there are total G number of green marbles and R number of red marbles.

            You can formulate two equations:

                        G + R = 120 ===> equation 1

            5/9 G + 2/7 R = 44 ===> equation 2

            From equation, you get

            35G + 18R = 44 × 9 × 7 = 2772 ===> equation 3

            From equation 1, G = 120 – R ===> equation 4

            So using equation 3 & 4, to find out R

            335 x 120 – 35R + 18R = 2772

            17R = 1428

            R = 84 ===> number of red marbles

            G = 120 – 84 = 36 ===> number of green marbles

            Number of big size green marbles = 36 x 4/9 = 16

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