A bag contained purple, grey and white staplers. ²₅ of the staplers were purple and ⁴₉ of the remainder were grey staplers.The rest were white staplers.

1. Find the ratio of the number of white staplers to the number of purple staplers.
2. There were 142 fewer grey staplers than purple staplers. How many staplers were there in the bag?

Purple staplers	Grey staplers	White staplers
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

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

Remaining fraction of grey staplers = ⁴₉
Remaining fraction of white staplers = 1 - ⁴₉ = ⁵₉

The total number of grey staplers and white staplers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 9 = 9

White staplers : Purple staplers
5 : 6

(b)
Difference in the number of purple staplers and grey staplers
= 6 u - 4 u
= 2 u

2 u = 142
1 u = 142 ÷ 2 = 71

Total number of staplers
= 6 u + 4 u + 5 u
= 15 u
= 15 x 71
= 1065

Answer(s): (a) 5 : 6; (b) 1065