A bag contained white, brown and gold notebooks. ²₅ of the notebooks were white and ⁴₉ of the remainder were brown notebooks.The rest were gold notebooks.

1. Find the ratio of the number of gold notebooks to the number of white notebooks.
2. There were 194 fewer brown notebooks than white notebooks. How many notebooks were there in the bag?

White notebooks	Brown notebooks	Gold notebooks
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

(a)
Fraction of white notebooks = ²₅
Fraction of notebooks that are not white = 1 - ²₅ = ³₅

Remaining fraction of brown notebooks = ⁴₉
Remaining fraction of gold notebooks = 1 - ⁴₉ = ⁵₉

The total number of brown notebooks and gold notebooks is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 9 = 9

Gold notebooks : White notebooks
5 : 6

(b)
Difference in the number of white notebooks and brown notebooks
= 6 u - 4 u
= 2 u

2 u = 194
1 u = 194 ÷ 2 = 97

Total number of notebooks
= 6 u + 4 u + 5 u
= 15 u
= 15 x 97
= 1455

Answer(s): (a) 5 : 6; (b) 1455