Riordan, Jenson and Carl had some cards in the ratio of 2 : 3 : 5. Carl gave 40% of his cards to Riordan and Jenson. As a result, Riordan had the same number of cards as Jenson and Carl had 24 fewer cards than Riordan.

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

Riordan	Jenson	Carl	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of cards that Carl gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of cards that Riordan and Jenson each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of cards that Riordan had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Riordan's cards after receiving from Carl
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 24
3.5 u - 3 u = 24
0.5 u = 24

1 u = 24 ÷ 0.5 = 48

Number of cards that Jenson had at first
= 3 u
= 3 x 48
= 144

Answer(s): (a) 75%; (b) 144