Betty had 75 beads. ²₅ were white and the rest were blue and silver. The ratio of the number of blue beads to the number of silver beads was 1 : 4. Betty 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 blue beads than white beads did he have at first?
2. How many more white beads did he have to buy?

White beads	Blue beads	Silver beads	Total
2x5	3x5
	1x3	4x3
10 u	3 u	12 u	75

	White beads	Blue beads	Silver beads
Before	10 u	3 u	12 u
Change	+ ?
After	15 u	15 u
Comparing white, blue and silver beads in the end	1	1

(a)
The total number of blue beads and silver beads is repeated. Make the total number of blue beads and silver 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 = 75

1 u = 75 ÷ 25 = 3

Number of less blue beads than white beads at first
= 10 u - 3 u
= 7 u
= 7 x 3
= 21

(b)
Number of more white beads that Betty had to buy
= 15 u - 10 u
= 5 u
= 5 x 3
= 15

Answer(s): (a) 21; (b) 15