Will had 350 beads. ⁴₇ were green and the rest were purple and grey. The ratio of the number of purple beads to the number of grey beads was 1 : 4. Will 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 purple beads did he have at first?
2. How many green beads did he have to give away?

Green beads	Purple beads	Grey beads	Total
4x5	3x5
	1x3	4x3
20 u	3 u	12 u	350

	Green beads	Purple beads	Grey beads
Before	20 u	3 u	12 u
Change	- ?
After	15 u	15 u
Comparing green, purple and grey beads in the end	1	1

(a)
The total number of purple beads and grey beads is repeated. Make the total number of purple beads and grey beads the same.  LCM of 3 and 5 is 15.

Total number of beads at first
= 20 u + 3 u + 12 u
= 35 u

35 u = 350

1 u = 350 ÷ 35 = 10

Number of more green beads than purple beads at first
= 20 u - 3 u
= 17 u
= 17 x 10
= 170

(b)
Number of more green beads that Will had to give away
= 20 u - 15 u
= 5 u
= 5 x 10
= 50

Answer(s): (a) 170; (b) 50