Warren had 120 beads. ³₅ were pink and the rest were gold and purple. The ratio of the number of gold beads to the number of purple beads was 1 : 5. Warren decided to give away some pink beads to decrease the number of pink beads to half of the total number of beads.

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

Pink beads	Gold beads	Purple beads	Total
3x3	2x3
	1x1	5x1
9 u	1 u	5 u	120

	Pink beads	Gold beads	Purple beads
Before	9 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing pink, gold and purple beads in the end	1	1

(a)
The total number of gold beads and purple beads is repeated. Make the total number of gold beads and purple beads the same.  LCM of 2 and 6 is 6.

Total number of beads at first
= 9 u + 1 u + 5 u
= 15 u

15 u = 120

1 u = 120 ÷ 15 = 8

Number of more pink beads than gold beads at first
= 9 u - 1 u
= 8 u
= 8 x 8
= 64

(b)
Number of more pink beads that Warren had to give away
= 9 u - 6 u
= 3 u
= 3 x 8
= 24

Answer(s): (a) 64; (b) 24