Lucy had 196 marbles. ²₇ were yellow and the rest were gold and grey. The ratio of the number of gold marbles to the number of grey marbles was 1 : 3. Lucy decided to buy some more yellow marbles to increase the number of yellow marbles to half of the total number of marbles.

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

Yellow marbles	Gold marbles	Grey marbles	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	196

	Yellow marbles	Gold marbles	Grey marbles
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing yellow, gold and grey marbles in the end	1	1

(a)
The total number of gold marbles and grey marbles is repeated. Make the total number of gold marbles and grey 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 gold marbles than yellow marbles at first
= 8 u - 5 u
= 3 u
= 3 x 7
= 21

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

Answer(s): (a) 21; (b) 84