Olivia had 168 erasers. ²₇ were silver and the rest were white and black. The ratio of the number of white erasers to the number of black erasers was 1 : 3. Olivia decided to buy some more silver erasers to increase the number of silver erasers to half of the total number of erasers.

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

Silver erasers	White erasers	Black erasers	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	168

	Silver erasers	White erasers	Black erasers
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing silver, white and black erasers in the end	1	1

(a)
The total number of white erasers and black erasers is repeated. Make the total number of white erasers and black erasers the same.  LCM of 5 and 4 is 20.

Total number of erasers at first
= 8 u + 5 u + 15 u
= 28 u

28 u = 168

1 u = 168 ÷ 28 = 6

Number of less white erasers than silver erasers at first
= 8 u - 5 u
= 3 u
= 3 x 6
= 18

(b)
Number of more silver erasers that Olivia had to buy
= 20 u - 8 u
= 12 u
= 12 x 6
= 72

Answer(s): (a) 18; (b) 72