Abi had some blue erasers and gold erasers in 2 boxes. In Box F, the ratio of the number of blue erasers to gold erasers was 8 : 3. In Box G, the number of blue erasers was 2 times the number of gold erasers. Abi transferred ²₃ of the gold erasers from Box F to Box G. The number of erasers in Box F became 135 and the ratio of the number of blue erasers to gold erasers in Box G became 4 : 5.

1. How many gold erasers were transferred from Box F to Box G?
2. What was the number of erasers in Box G after the transfer?

	Box F		Box G
	Blue	Gold	Blue	Gold
Comparing blue erasers and gold erasers at first	8 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing blue erasers and gold erasers in the end	8 u	1 u	4 p	5 p

(a)
Total number of erasers in the end for Box F
= 8 u + 1 u
= 9 u

9 u = 135

1 u = 135 ÷ 9 = 15

Number of gold erasers that were transferred from Box F to Box G
= 2 u
= 2 x 15
= 30

(b)
The number of blue erasers in Box G remains unchanged.  Make the number of blue erasers in Box G the same.  LCM of 2 and 4 is 4. 

Increase in the number of gold erasers in Box G
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 30

1 p = 30 ÷ 3 = 10

Number of erasers in Box G in the end
= 4 p + 5 p
= 9 p
= 9 x 10
= 90

Answer(s): (a) 30; (b) 90