Roshel had 147 beads. ³₇ were purple and the rest were silver and white. The ratio of the number of silver beads to the number of white beads was 1 : 2. Roshel decided to buy some more purple beads to increase the number of purple beads to half of the total number of beads.

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

Purple beads	Silver beads	White beads	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	147

	Purple beads	Silver beads	White beads
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing purple, silver and white beads in the end	1	1

(a)
The total number of silver beads and white beads is repeated. Make the total number of silver beads and white beads the same.  LCM of 4 and 3 is 12.

Total number of beads at first
= 9 u + 4 u + 8 u
= 21 u

21 u = 147

1 u = 147 ÷ 21 = 7

Number of less silver beads than purple beads at first
= 9 u - 4 u
= 5 u
= 5 x 7
= 35

(b)
Number of more purple beads that Roshel had to buy
= 12 u - 9 u
= 3 u
= 3 x 7
= 21

Answer(s): (a) 35; (b) 21