Jenson, Luke and Cole had some cards in the ratio of 2 : 3 : 5. Cole gave 50% of his cards to Jenson and Luke. As a result, Jenson had the same number of cards as Luke and Cole had 40 fewer cards than Jenson.

1. What was the percentage increase in Jenson's cards after receiving from Cole?
2. How many cards did Luke have at first?

Jenson	Luke	Cole	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 Cole gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that Jenson and Luke 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 Jenson had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of cards that Luke had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96