Elyse had 196 marbles. ²₇ were silver and the rest were green and red. The ratio of the number of green marbles to the number of red marbles was 1 : 3. Elyse decided to buy some more silver marbles to increase the number of silver marbles to half of the total number of marbles.

1. How many less green marbles than silver marbles did he have at first?
2. How many more silver marbles did he have to buy?

Silver marbles	Green marbles	Red marbles	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	196

	Silver marbles	Green marbles	Red marbles
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing silver, green and red marbles in the end	1	1

(a)
The total number of green marbles and red marbles is repeated. Make the total number of green marbles and red marbles the same.  LCM of 5 and 4 is 20.

Total number of marbles at first
= 8 u + 5 u + 15 u
= 28 u

28 u = 196

1 u = 196 ÷ 28 = 7

Number of less green marbles than silver marbles at first
= 8 u - 5 u
= 3 u
= 3 x 7
= 21

(b)
Number of more silver marbles that Elyse had to buy
= 20 u - 8 u
= 12 u
= 12 x 7
= 84

Answer(s): (a) 21; (b) 84