Xavier had 120 beads. ⁵₆ were green and the rest were brown and grey. The ratio of the number of brown beads to the number of grey beads was 1 : 4. Xavier decided to give away some green beads to decrease the number of green beads to half of the total number of beads.

1. How many more green beads than brown beads did he have at first?
2. How many green beads did he have to give away?

Green beads	Brown beads	Grey beads	Total
5x5	1x5
	1x1	4x1
25 u	1 u	4 u	120

	Green beads	Brown beads	Grey beads
Before	25 u	1 u	4 u
Change	- ?
After	5 u	5 u
Comparing green, brown and grey beads in the end	1	1

(a)
The total number of brown beads and grey beads is repeated. Make the total number of brown beads and grey beads the same.  LCM of 1 and 5 is 5.

Total number of beads at first
= 25 u + 1 u + 4 u
= 30 u

30 u = 120

1 u = 120 ÷ 30 = 4

Number of more green beads than brown beads at first
= 25 u - 1 u
= 24 u
= 24 x 4
= 96

(b)
Number of more green beads that Xavier had to give away
= 25 u - 5 u
= 20 u
= 20 x 4
= 80

Answer(s): (a) 96; (b) 80