Olivia had 315 pens. ³₇ were grey and the rest were yellow and gold. The ratio of the number of yellow pens to the number of gold pens was 1 : 4. Olivia decided to buy some more grey pens to increase the number of grey pens to half of the total number of pens.

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

Grey pens	Yellow pens	Gold pens	Total
3x5	4x5
	1x4	4x4
15 u	4 u	16 u	315

	Grey pens	Yellow pens	Gold pens
Before	15 u	4 u	16 u
Change	+ ?
After	20 u	20 u
Comparing grey, yellow and gold pens in the end	1	1

(a)
The total number of yellow pens and gold pens is repeated. Make the total number of yellow pens and gold 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 = 315

1 u = 315 ÷ 35 = 9

Number of less yellow pens than grey pens at first
= 15 u - 4 u
= 11 u
= 11 x 9
= 99

(b)
Number of more grey pens that Olivia had to buy
= 20 u - 15 u
= 5 u
= 5 x 9
= 45

Answer(s): (a) 99; (b) 45