Emma had 105 beads. ³₇ were blue and the rest were green and yellow. The ratio of the number of green beads to the number of yellow beads was 1 : 2. Emma decided to buy some more blue beads to increase the number of blue beads to half of the total number of beads.

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

Blue beads	Green beads	Yellow beads	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	105

	Blue beads	Green beads	Yellow beads
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing blue, green and yellow beads in the end	1	1

(a)
The total number of green beads and yellow beads is repeated. Make the total number of green beads and yellow 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 = 105

1 u = 105 ÷ 21 = 5

Number of less green beads than blue beads at first
= 9 u - 4 u
= 5 u
= 5 x 5
= 25

(b)
Number of more blue beads that Emma had to buy
= 12 u - 9 u
= 3 u
= 3 x 5
= 15

Answer(s): (a) 25; (b) 15