A bag contained gold, grey and green staplers. ⁴₅ of the staplers were gold and ⁵₈ of the remainder were grey staplers.The rest were green staplers.

1. Find the ratio of the number of green staplers to the number of gold staplers.
2. There were 162 fewer grey staplers than gold staplers. How many staplers were there in the bag?

Gold staplers	Grey staplers	Green staplers
4x8	1x8
	5x1	3x1
32 u	5 u	3 u

(a)
Fraction of gold staplers = ⁴₅
Fraction of staplers that are not gold = 1 - ⁴₅ = ¹₅

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

The total number of grey staplers and green staplers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 1 and 8 = 8

Green staplers : Gold staplers
3 : 32

(b)
Difference in the number of gold staplers and grey staplers
= 32 u - 5 u
= 27 u

27 u = 162
1 u = 162 ÷ 27 = 6

Total number of staplers
= 32 u + 5 u + 3 u
= 40 u
= 40 x 6
= 240

Answer(s): (a) 3 : 32; (b) 240