Carl had 54 pencils. ⁵₆ were purple and the rest were gold and white. The ratio of the number of gold pencils to the number of white pencils was 1 : 2. Carl decided to give away some purple pencils to decrease the number of purple pencils to half of the total number of pencils.

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

Purple pencils	Gold pencils	White pencils	Total
5x3	1x3
	1x1	2x1
15 u	1 u	2 u	54

	Purple pencils	Gold pencils	White pencils
Before	15 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing purple, gold and white pencils in the end	1	1

(a)
The total number of gold pencils and white pencils is repeated. Make the total number of gold pencils and white pencils the same.  LCM of 1 and 3 is 3.

Total number of pencils at first
= 15 u + 1 u + 2 u
= 18 u

18 u = 54

1 u = 54 ÷ 18 = 3

Number of more purple pencils than gold pencils at first
= 15 u - 1 u
= 14 u
= 14 x 3
= 42

(b)
Number of more purple pencils that Carl had to give away
= 15 u - 3 u
= 12 u
= 12 x 3
= 36

Answer(s): (a) 42; (b) 36