Esther had 175 beads. ²₅ were white and the rest were purple and green. The ratio of the number of purple beads to the number of green beads was 1 : 4. Esther decided to buy some more white beads to increase the number of white beads to half of the total number of beads.

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

White beads	Purple beads	Green beads	Total
2x5	3x5
	1x3	4x3
10 u	3 u	12 u	175

	White beads	Purple beads	Green beads
Before	10 u	3 u	12 u
Change	+ ?
After	15 u	15 u
Comparing white, purple and green beads in the end	1	1

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

Total number of beads at first
= 10 u + 3 u + 12 u
= 25 u

25 u = 175

1 u = 175 ÷ 25 = 7

Number of less purple beads than white beads at first
= 10 u - 3 u
= 7 u
= 7 x 7
= 49

(b)
Number of more white beads that Esther had to buy
= 15 u - 10 u
= 5 u
= 5 x 7
= 35

Answer(s): (a) 49; (b) 35