In April, Olivia and Charlie had cards in the ratio 5 : 2. In May, each of them gave away the same number of cards. Olivia then had five times as many cards as Charlie.

1. Find the ratio of the number of cards Charlie had in April to the number of cards he had in May.
2. Find the ratio of the total number of cards both had in April to the total number of cards both had in May.

	Olivia	Charlie	Difference
Before	5x4 = 20 u	2x4 = 8 u	3x4 = 12 u
Change	- 5 u	- 5 u
After	5x3 = 15 u	1x3 = 3 u	4x3 = 12 u

(a)
Since Olivia and Charlie gave away the same number of cards, the difference in the number of cards between Olivia and Charlie at first and in the end remains the same.

Make the difference in the number of cards at first and in the end the same. LCM of 3 and 4 is 12.

Charlie's cards in April : Charlie's cards in May
8 : 3

(b)
Total number of cards in April
= 20 u + 8 u
= 28 u

Total number of cards in May
= 15 u + 3 u
= 18 u

Total cards in April : Total cards in May
28 : 18 _(÷2)
14 : 9 

Answer(s): (a) 8 : 3; (b) 14 : 9