Seth had 48 erasers. ³₄ were pink and the rest were purple and green. The ratio of the number of purple erasers to the number of green erasers was 1 : 5. Seth decided to give away some pink erasers to decrease the number of pink erasers to half of the total number of erasers.

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

Pink erasers	Purple erasers	Green erasers	Total
3x6	1x6
	1x1	5x1
18 u	1 u	5 u	48

	Pink erasers	Purple erasers	Green erasers
Before	18 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing pink, purple and green erasers in the end	1	1

(a)
The total number of purple erasers and green erasers is repeated. Make the total number of purple erasers and green erasers the same.  LCM of 1 and 6 is 6.

Total number of erasers at first
= 18 u + 1 u + 5 u
= 24 u

24 u = 48

1 u = 48 ÷ 24 = 2

Number of more pink erasers than purple erasers at first
= 18 u - 1 u
= 17 u
= 17 x 2
= 34

(b)
Number of more pink erasers that Seth had to give away
= 18 u - 6 u
= 12 u
= 12 x 2
= 24

Answer(s): (a) 34; (b) 24