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

1. Find the ratio of the number of white staplers to the number of grey staplers.
2. There were 162 fewer silver staplers than grey staplers. How many staplers were there in the packet?

Grey staplers	Silver staplers	White staplers
3x4	2x4
	3x1	5x1
12 u	3 u	5 u

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

Remaining fraction of silver staplers = ³₈
Remaining fraction of white staplers = 1 - ³₈ = ⁵₈

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

White staplers : Grey staplers
5 : 12

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

9 u = 162
1 u = 162 ÷ 9 = 18

Total number of staplers
= 12 u + 3 u + 5 u
= 20 u
= 20 x 18
= 360

Answer(s): (a) 5 : 12; (b) 360