Min had 231 pencils. ³₇ were red and the rest were brown and gold. The ratio of the number of brown pencils to the number of gold pencils was 1 : 5. Min decided to buy some more red pencils to increase the number of red pencils to half of the total number of pencils.

1. How many less brown pencils than red pencils did he have at first?
2. How many more red pencils did he have to buy?

Red pencils	Brown pencils	Gold pencils	Total
3x3	4x3
	1x2	5x2
9 u	2 u	10 u	231

	Red pencils	Brown pencils	Gold pencils
Before	9 u	2 u	10 u
Change	+ ?
After	12 u	12 u
Comparing red, brown and gold pencils in the end	1	1

(a)
The total number of brown pencils and gold pencils is repeated. Make the total number of brown pencils and gold pencils the same.  LCM of 4 and 6 is 12.

Total number of pencils at first
= 9 u + 2 u + 10 u
= 21 u

21 u = 231

1 u = 231 ÷ 21 = 11

Number of less brown pencils than red pencils at first
= 9 u - 2 u
= 7 u
= 7 x 11
= 77

(b)
Number of more red pencils that Min had to buy
= 12 u - 9 u
= 3 u
= 3 x 11
= 33

Answer(s): (a) 77; (b) 33