Shannon had 240 erasers. ²₅ were purple and the rest were pink and blue. The ratio of the number of pink erasers to the number of blue erasers was 1 : 3. Shannon decided to buy some more purple erasers to increase the number of purple erasers to half of the total number of erasers.

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

Purple erasers	Pink erasers	Blue erasers	Total
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	240

	Purple erasers	Pink erasers	Blue erasers
Before	8 u	3 u	9 u
Change	+ ?
After	12 u	12 u
Comparing purple, pink and blue erasers in the end	1	1

(a)
The total number of pink erasers and blue erasers is repeated. Make the total number of pink erasers and blue erasers the same.  LCM of 3 and 4 is 12.

Total number of erasers at first
= 8 u + 3 u + 9 u
= 20 u

20 u = 240

1 u = 240 ÷ 20 = 12

Number of less pink erasers than purple erasers at first
= 8 u - 3 u
= 5 u
= 5 x 12
= 60

(b)
Number of more purple erasers that Shannon had to buy
= 12 u - 8 u
= 4 u
= 4 x 12
= 48

Answer(s): (a) 60; (b) 48