Lee, Asher and Brandon had some cards in the ratio of 2 : 3 : 5. Brandon gave 50% of his cards to Lee and Asher. As a result, Lee had the same number of cards as Asher and Brandon had 20 fewer cards than Lee.

1. What was the percentage increase in Lee's cards after receiving from Brandon?
2. How many cards did Asher have at first?

Lee	Asher	Brandon	Total
2 u	3 u	5 u	10 u
+ 2.5 u		- 2.5 u
3.75 u	3.75 u	2.5 u	10 u

(a)
Number of cards that Brandon gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that Lee and Asher each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of cards that Lee had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Lee's cards after receiving from Brandon
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 20
3.75 u - 2.5 u = 20
1.25 u = 20

1 u = 20 ÷ 1.25 = 16

Number of cards that Asher had at first
= 3 u
= 3 x 16
= 48

Answer(s): (a) 87.5%; (b) 48