Billy had 175 pencils. ⁵₇ were white and the rest were purple and grey. The ratio of the number of purple pencils to the number of grey pencils was 1 : 4. Billy decided to give away some white pencils to decrease the number of white pencils to half of the total number of pencils.

1. How many more white pencils than purple pencils did he have at first?
2. How many white pencils did he have to give away?

White pencils	Purple pencils	Grey pencils	Total
5x5	2x5
	1x2	4x2
25 u	2 u	8 u	175

	White pencils	Purple pencils	Grey pencils
Before	25 u	2 u	8 u
Change	- ?
After	10 u	10 u
Comparing white, purple and grey pencils in the end	1	1

(a)
The total number of purple pencils and grey pencils is repeated. Make the total number of purple pencils and grey pencils the same.  LCM of 2 and 5 is 10.

Total number of pencils at first
= 25 u + 2 u + 8 u
= 35 u

35 u = 175

1 u = 175 ÷ 35 = 5

Number of more white pencils than purple pencils at first
= 25 u - 2 u
= 23 u
= 23 x 5
= 115

(b)
Number of more white pencils that Billy had to give away
= 25 u - 10 u
= 15 u
= 15 x 5
= 75

Answer(s): (a) 115; (b) 75