A bag contained brown, purple and silver markers. ⁴₅ of the markers were brown and ³₈ of the remainder were purple markers.The rest were silver markers.

1. Find the ratio of the number of silver markers to the number of brown markers.
2. There were 145 fewer purple markers than brown markers. How many markers were there in the bag?

Brown markers	Purple markers	Silver markers
4x8	1x8
	3x1	5x1
32 u	3 u	5 u

(a)
Fraction of brown markers = ⁴₅
Fraction of markers that are not brown = 1 - ⁴₅ = ¹₅

Remaining fraction of purple markers = ³₈
Remaining fraction of silver markers = 1 - ³₈ = ⁵₈

The total number of purple markers and silver markers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 1 and 8 = 8

Silver markers : Brown markers
5 : 32

(b)
Difference in the number of brown markers and purple markers
= 32 u - 3 u
= 29 u

29 u = 145
1 u = 145 ÷ 29 = 5

Total number of markers
= 32 u + 3 u + 5 u
= 40 u
= 40 x 5
= 200

Answer(s): (a) 5 : 32; (b) 200