A bag contained blue, purple and silver staplers. ³₅ of the staplers were blue and ⁴₉ of the remainder were purple staplers.The rest were silver staplers.

1. Find the ratio of the number of silver staplers to the number of blue staplers.
2. There were 171 fewer purple staplers than blue staplers. How many staplers were there in the bag?

Blue staplers	Purple staplers	Silver staplers
3x9	2x9
	4x2	5x2
27 u	8 u	10 u

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

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

The total number of purple staplers and silver staplers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 2 and 9 = 18

Silver staplers : Blue staplers
10 : 27

(b)
Difference in the number of blue staplers and purple staplers
= 27 u - 8 u
= 19 u

19 u = 171
1 u = 171 ÷ 19 = 9

Total number of staplers
= 27 u + 8 u + 10 u
= 45 u
= 45 x 9
= 405

Answer(s): (a) 10 : 27; (b) 405