A bag contained black, yellow and silver markers. ⁴₅ of the markers were black and ⁴₉ of the remainder were yellow markers.The rest were silver markers.

1. Find the ratio of the number of silver markers to the number of black markers.
2. There were 160 fewer yellow markers than black markers. How many markers were there in the bag?

Black markers	Yellow markers	Silver markers
4x9	1x9
	4x1	5x1
36 u	4 u	5 u

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

Remaining fraction of yellow markers = ⁴₉
Remaining fraction of silver markers = 1 - ⁴₉ = ⁵₉

The total number of yellow markers and silver markers is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 1 and 9 = 9

Silver markers : Black markers
5 : 36

(b)
Difference in the number of black markers and yellow markers
= 36 u - 4 u
= 32 u

32 u = 160
1 u = 160 ÷ 32 = 5

Total number of markers
= 36 u + 4 u + 5 u
= 45 u
= 45 x 5
= 225

Answer(s): (a) 5 : 36; (b) 225