Gabriel had 252 coins. ⁵₇ were grey and the rest were blue and yellow. The ratio of the number of blue coins to the number of yellow coins was 1 : 5. Gabriel decided to give away some grey coins to decrease the number of grey coins to half of the total number of coins.

1. How many more grey coins than blue coins did he have at first?
2. How many grey coins did he have to give away?

Grey coins	Blue coins	Yellow coins	Total
5x3	2x3
	1x1	5x1
15 u	1 u	5 u	252

	Grey coins	Blue coins	Yellow coins
Before	15 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing grey, blue and yellow coins in the end	1	1

(a)
The total number of blue coins and yellow coins is repeated. Make the total number of blue coins and yellow coins the same.  LCM of 2 and 6 is 6.

Total number of coins at first
= 15 u + 1 u + 5 u
= 21 u

21 u = 252

1 u = 252 ÷ 21 = 12

Number of more grey coins than blue coins at first
= 15 u - 1 u
= 14 u
= 14 x 12
= 168

(b)
Number of more grey coins that Gabriel had to give away
= 15 u - 6 u
= 9 u
= 9 x 12
= 108

Answer(s): (a) 168; (b) 108