Barbara had 294 pens. ²₇ were brown and the rest were pink and blue. The ratio of the number of pink pens to the number of blue pens was 1 : 5. Barbara decided to buy some more brown pens to increase the number of brown pens to half of the total number of pens.

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

Brown pens	Pink pens	Blue pens	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	294

	Brown pens	Pink pens	Blue pens
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing brown, pink and blue pens in the end	1	1

(a)
The total number of pink pens and blue pens is repeated. Make the total number of pink pens and blue pens the same.  LCM of 5 and 6 is 30.

Total number of pens at first
= 12 u + 5 u + 25 u
= 42 u

42 u = 294

1 u = 294 ÷ 42 = 7

Number of less pink pens than brown pens at first
= 12 u - 5 u
= 7 u
= 7 x 7
= 49

(b)
Number of more brown pens that Barbara had to buy
= 30 u - 12 u
= 18 u
= 18 x 7
= 126

Answer(s): (a) 49; (b) 126