In April, Opal and Brandon had cards in the ratio 3 : 2. In May, each of them gave away the same number of cards. Opal then had four times as many cards as Brandon.

1. Find the ratio of the number of cards Brandon 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.

	Opal	Brandon	Difference
Before	3x3 = 9 u	2x3 = 6 u	1x3 = 3 u
Change	- 5 u	- 5 u
After	4x1 = 4 u	1x1 = 1 u	3x1 = 3 u

(a)
Since Opal and Brandon gave away the same number of cards, the difference in the number of cards between Opal and Brandon 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 1 and 3 is 3.

Brandon's cards in April : Brandon's cards in May
6 : 1

(b)
Total number of cards in April
= 9 u + 6 u
= 15 u

Total number of cards in May
= 4 u + 1 u
= 5 u

Total cards in April : Total cards in May
15 : 5 _(÷5)
3 : 1 

Answer(s): (a) 6 : 1; (b) 3 : 1