Anna had 42 marbles. ³₇ were pink and the rest were purple and gold. The ratio of the number of purple marbles to the number of gold marbles was 1 : 2. Anna decided to buy some more pink marbles to increase the number of pink marbles to half of the total number of marbles.

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

Pink marbles	Purple marbles	Gold marbles	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	42

	Pink marbles	Purple marbles	Gold marbles
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing pink, purple and gold marbles in the end	1	1

(a)
The total number of purple marbles and gold marbles is repeated. Make the total number of purple marbles and gold marbles the same.  LCM of 4 and 3 is 12.

Total number of marbles at first
= 9 u + 4 u + 8 u
= 21 u

21 u = 42

1 u = 42 ÷ 21 = 2

Number of less purple marbles than pink marbles at first
= 9 u - 4 u
= 5 u
= 5 x 2
= 10

(b)
Number of more pink marbles that Anna had to buy
= 12 u - 9 u
= 3 u
= 3 x 2
= 6

Answer(s): (a) 10; (b) 6