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

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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.

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