Oliver had 288 marbles. ⁵₆ were silver and the rest were brown and gold. The ratio of the number of brown marbles to the number of gold marbles was 1 : 5. Oliver decided to give away some silver marbles to decrease the number of silver marbles to half of the total number of marbles.

1. How many more silver marbles than brown marbles did he have at first?
2. How many silver marbles did he have to give away?

Silver marbles	Brown marbles	Gold marbles	Total
5x6	1x6
	1x1	5x1
30 u	1 u	5 u	288

	Silver marbles	Brown marbles	Gold marbles
Before	30 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing silver, brown and gold marbles in the end	1	1

(a)
The total number of brown marbles and gold marbles is repeated. Make the total number of brown marbles and gold marbles the same.  LCM of 1 and 6 is 6.

Total number of marbles at first
= 30 u + 1 u + 5 u
= 36 u

36 u = 288

1 u = 288 ÷ 36 = 8

Number of more silver marbles than brown marbles at first
= 30 u - 1 u
= 29 u
= 29 x 8
= 232

(b)
Number of more silver marbles that Oliver had to give away
= 30 u - 6 u
= 24 u
= 24 x 8
= 192

Answer(s): (a) 232; (b) 192