There were 87 gold, black and yellow markers in a box. 7 yellow markers were removed from the box and the ratio of the number of gold markers to the number of black markers to the number of yellow markers became 5 : 2 : 3. Then some purple markers were added and the ratio of the number of yellow markers to the number of purple markers was 3 : 9.

1. What was the ratio of the number of gold markers to the number of black markers to the number of yellow markers at first?
2. How many markers were in the box in the end?

	Gold	Black	Yellow	Purple	Total
Before	5 u	2 u	3 u + 7	0	87
Change 1	No change	No change	- 7		- 7
After 1	5 u	2 u	3 u		80
Change 2	No change	No change	No change	+ 9 u
After 2	5 u	2 u	3 u	9 u

(a)
Total number of markers at first
= 5 u + 2 u + 3 u + 7
= 10 u + 7

10 u + 7 = 87
10 u = 87 - 7
10 u = 80

1 u = 80 ÷ 10 = 8

Number of gold markers at first
= 5 u
= 5 x 8
= 40

Number of black markers at first
= 2 u
= 2 x 8
= 16

Number of yellow markers at first
= 3 u + 7
= 3 x 8 + 7
= 31 

At first
Gold markers : Black markers : Yellow markers
40 : 16 : 31

(b)
Total number of markers in the box in the end
= 5 u + 2 u + 3 u + 9 u
= 19 u
= 152

Answer(s): (a) 40 : 16 : 31; (b) 152