Asher had 144 beads. ⁵₆ were silver and the rest were purple and pink. The ratio of the number of purple beads to the number of pink beads was 1 : 2. Asher decided to give away some silver beads to decrease the number of silver beads to half of the total number of beads.

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

Silver beads	Purple beads	Pink beads	Total
5x3	1x3
	1x1	2x1
15 u	1 u	2 u	144

	Silver beads	Purple beads	Pink beads
Before	15 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing silver, purple and pink beads in the end	1	1

(a)
The total number of purple beads and pink beads is repeated. Make the total number of purple beads and pink beads the same.  LCM of 1 and 3 is 3.

Total number of beads at first
= 15 u + 1 u + 2 u
= 18 u

18 u = 144

1 u = 144 ÷ 18 = 8

Number of more silver beads than purple beads at first
= 15 u - 1 u
= 14 u
= 14 x 8
= 112

(b)
Number of more silver beads that Asher had to give away
= 15 u - 3 u
= 12 u
= 12 x 8
= 96

Answer(s): (a) 112; (b) 96