A packet contained blue, purple and grey staplers. ³₅ of the staplers were blue and ³₈ of the remainder were purple staplers.The rest were grey staplers.

1. Find the ratio of the number of grey staplers to the number of blue staplers.
2. There were 144 fewer purple staplers than blue staplers. How many staplers were there in the packet?

Blue staplers	Purple staplers	Grey staplers
3x4	2x4
	3x1	5x1
12 u	3 u	5 u

(a)
Fraction of blue staplers = ³₅
Fraction of staplers that are not blue = 1 - ³₅ = ²₅

Remaining fraction of purple staplers = ³₈
Remaining fraction of grey staplers = 1 - ³₈ = ⁵₈

The total number of purple staplers and grey staplers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 2 and 8 = 8

Grey staplers : Blue staplers
5 : 12

(b)
Difference in the number of blue staplers and purple staplers
= 12 u - 3 u
= 9 u

9 u = 144
1 u = 144 ÷ 9 = 16

Total number of staplers
= 12 u + 3 u + 5 u
= 20 u
= 20 x 16
= 320

Answer(s): (a) 5 : 12; (b) 320