Cindy had 189 beads. ³₇ were pink and the rest were grey and black. The ratio of the number of grey beads to the number of black beads was 1 : 2. Cindy decided to buy some more pink beads to increase the number of pink beads to half of the total number of beads.

1. How many less grey beads than pink beads did he have at first?
2. How many more pink beads did he have to buy?

Pink beads	Grey beads	Black beads	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	189

	Pink beads	Grey beads	Black beads
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing pink, grey and black beads in the end	1	1

(a)
The total number of grey beads and black beads is repeated. Make the total number of grey beads and black beads the same.  LCM of 4 and 3 is 12.

Total number of beads at first
= 9 u + 4 u + 8 u
= 21 u

21 u = 189

1 u = 189 ÷ 21 = 9

Number of less grey beads than pink beads at first
= 9 u - 4 u
= 5 u
= 5 x 9
= 45

(b)
Number of more pink beads that Cindy had to buy
= 12 u - 9 u
= 3 u
= 3 x 9
= 27

Answer(s): (a) 45; (b) 27