Glen had 288 beads. ⁵₆ were purple and the rest were pink and black. The ratio of the number of pink beads to the number of black beads was 1 : 3. Glen decided to give away some purple beads to decrease the number of purple beads to half of the total number of beads.

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

Purple beads	Pink beads	Black beads	Total
5x4	1x4
	1x1	3x1
20 u	1 u	3 u	288

	Purple beads	Pink beads	Black beads
Before	20 u	1 u	3 u
Change	- ?
After	4 u	4 u
Comparing purple, pink and black beads in the end	1	1

(a)
The total number of pink beads and black beads is repeated. Make the total number of pink beads and black beads the same.  LCM of 1 and 4 is 4.

Total number of beads at first
= 20 u + 1 u + 3 u
= 24 u

24 u = 288

1 u = 288 ÷ 24 = 12

Number of more purple beads than pink beads at first
= 20 u - 1 u
= 19 u
= 19 x 12
= 228

(b)
Number of more purple beads that Glen had to give away
= 20 u - 4 u
= 16 u
= 16 x 12
= 192

Answer(s): (a) 228; (b) 192