A packet contained brown, gold and white staplers. ³₅ of the staplers were brown and ⁴₅ of the remainder were gold staplers.The rest were white staplers.

1. Find the ratio of the number of white staplers to the number of brown staplers.
2. There were 175 fewer gold staplers than brown staplers. How many staplers were there in the packet?

Brown staplers	Gold staplers	White staplers
3x5	2x5
	4x2	1x2
15 u	8 u	2 u

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

Remaining fraction of gold staplers = ⁴₅
Remaining fraction of white staplers = 1 - ⁴₅ = ¹₅

The total number of gold staplers and white staplers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 2 and 5 = 10

White staplers : Brown staplers
2 : 15

(b)
Difference in the number of brown staplers and gold staplers
= 15 u - 8 u
= 7 u

7 u = 175
1 u = 175 ÷ 7 = 25

Total number of staplers
= 15 u + 8 u + 2 u
= 25 u
= 25 x 25
= 625

Answer(s): (a) 2 : 15; (b) 625