Jane had 385 pens. ³₇ were purple and the rest were yellow and pink. The ratio of the number of yellow pens to the number of pink pens was 1 : 4. Jane decided to buy some more purple pens to increase the number of purple pens to half of the total number of pens.

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

Purple pens	Yellow pens	Pink pens	Total
3x5	4x5
	1x4	4x4
15 u	4 u	16 u	385

	Purple pens	Yellow pens	Pink pens
Before	15 u	4 u	16 u
Change	+ ?
After	20 u	20 u
Comparing purple, yellow and pink pens in the end	1	1

(a)
The total number of yellow pens and pink pens is repeated. Make the total number of yellow pens and pink pens the same.  LCM of 4 and 5 is 20.

Total number of pens at first
= 15 u + 4 u + 16 u
= 35 u

35 u = 385

1 u = 385 ÷ 35 = 11

Number of less yellow pens than purple pens at first
= 15 u - 4 u
= 11 u
= 11 x 11
= 121

(b)
Number of more purple pens that Jane had to buy
= 20 u - 15 u
= 5 u
= 5 x 11
= 55

Answer(s): (a) 121; (b) 55