A packet contained blue, pink and black markers. ²₅ of the markers were blue and ⁴₉ of the remainder were pink markers.The rest were black markers.

1. Find the ratio of the number of black markers to the number of blue markers.
2. There were 164 fewer pink markers than blue markers. How many markers were there in the packet?

Blue markers	Pink markers	Black markers
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

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

Remaining fraction of pink markers = ⁴₉
Remaining fraction of black markers = 1 - ⁴₉ = ⁵₉

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

Black markers : Blue markers
5 : 6

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

2 u = 164
1 u = 164 ÷ 2 = 82

Total number of markers
= 6 u + 4 u + 5 u
= 15 u
= 15 x 82
= 1230

Answer(s): (a) 5 : 6; (b) 1230