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Upper primary school mathematics question UPQ88

Fatimah has a bag of marbles and a bag of beads to use in CongKak games. There are equal number of marbles and beads. The marbles and the beads are either green or yellow. She has 3 times as many green marbles as green beads and the number of yellow marbles is 5/8 the number of yellow beads.

(a) What is the ratio of the number of green beads to the number of yellow marbles?

(b) If she has total 240 of green marbles and green beads, what is the total number of marbles and beads in the two bags?

Solution:

We can draw models base on equal number of marbles and beads as well the ratio of the different colours of the marbles and beads as below:

Given number of green marbles (GM) is 3 times number of green beads (GB)

Given number of yellow marbles (YM) is 5/8 the number of yellow beads (YB)

Also number of marble (M) equal to number of beads (B)

M = B

GM + YM = YB + GB

GM – GB = YB – YM

From the above models,

2 units of GM = 3 units of YB

1 unit of GM = 3/2 units of YB = 1 unit of GB

Ratio of the number of green beads to the number of yellow marbles = GM : YM = 3/2 : 5 = 3 : 10

Total green marbles (GM) and green beads (GB) = 240

4 green units = 240

1 green unit = 60

2 green units = 2 × 60 = 120 = 3 yellow units

1 yellow unit = 40

Total number of marbles and beads = 19 yellow units = 19 × 40 = 760

Alternative solution:

Number of marble (M) equal to number of beads (B)

M : B = 1 : 1

(GM + YM) : (GB + YB) = 1 : 1 G : green and Y : yellow

Given green marbles (GM) is 3 times green beads (GB)

GM = 3GB

Given yellow marbles (YM) is 5/8 of yellow beads (YB)

YM = 5/8 YB **==>** YB = 8/5 YM

(GM + YM) : (GB + YB) = 1 : 1

GM + YM = GB + YB

3GB + YM = GB + 8/5 YM

2GB = 3/5 YM

GB = 3/10 YM **==>** GB : YM = 3 : 10

GM = 3GB = 9/10 YM **==>** GM : YM = 9 : 10

YB = 8/5 YM **==>** YB : YM = 8 : 5 = 16 : 10

We have,

GM : GB : YM : YB = 9 : 3 : 10 : 16

Total green marbles (GM) and green beads (GB) = 240

12 units = 240

1 unit = 20

Total marbles and beads = 38 × 20 = 760