A packet contained green, pink and purple staplers. ²₅ of the staplers were green and ⁴₉ of the remainder were pink staplers.The rest were purple staplers.

1. Find the ratio of the number of purple staplers to the number of green staplers.
2. There were 186 fewer pink staplers than green staplers. How many staplers were there in the packet?

Green staplers	Pink staplers	Purple staplers
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

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

Remaining fraction of pink staplers = ⁴₉
Remaining fraction of purple staplers = 1 - ⁴₉ = ⁵₉

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

Purple staplers : Green staplers
5 : 6

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

2 u = 186
1 u = 186 ÷ 2 = 93

Total number of staplers
= 6 u + 4 u + 5 u
= 15 u
= 15 x 93
= 1395

Answer(s): (a) 5 : 6; (b) 1395