A packet contained green, silver and black staplers. ³₅ of the staplers were green and ¹₈ of the remainder were silver staplers.The rest were black staplers.

1. Find the ratio of the number of black staplers to the number of green staplers.
2. There were 187 fewer silver staplers than green staplers. How many staplers were there in the packet?

Green staplers	Silver staplers	Black staplers
3x4	2x4
	1x1	7x1
12 u	1 u	7 u

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

Remaining fraction of silver staplers = ¹₈
Remaining fraction of black staplers = 1 - ¹₈ = ⁷₈

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

Black staplers : Green staplers
7 : 12

(b)
Difference in the number of green staplers and silver staplers
= 12 u - 1 u
= 11 u

11 u = 187
1 u = 187 ÷ 11 = 17

Total number of staplers
= 12 u + 1 u + 7 u
= 20 u
= 20 x 17
= 340

Answer(s): (a) 7 : 12; (b) 340