Valen, Paul and Sean had some cards in the ratio of 5 : 6 : 11. Sean gave 40% of his cards to Valen and Paul. As a result, Valen had the same number of cards as Paul and Sean had 44 fewer cards than Valen.

1. What was the percentage increase in Valen's cards after receiving from Sean?
2. How many cards did Paul have at first?

Valen	Paul	Sean	Total
5 u	6 u	11 u	22 u
+ 4.4 u		- 4.4 u
7.7 u	7.7 u	6.6 u	22 u

(a)
Number of cards that Sean gave away
= 40% x 11
= ⁴⁰₁₀₀ x 11
= 4.4 u

Number of cards that Valen and Paul each had in the end
= (22 u - 6.6 u) ÷ 2
= 15.4 u ÷ 2
= 7.7 u

Increase in the number of cards that Valen had
= 7.7 u - 5 u
= 2.7 u

Percentage increase in Valen's cards after receiving from Sean
= ^2.7₅ x 100%
= 54%

(b)
7.7 u = 6.6 u + 44
7.7 u - 6.6 u = 44
1.1 u = 44

1 u = 44 ÷ 1.1 = 40

Number of cards that Paul had at first
= 6 u
= 6 x 40
= 240

Answer(s): (a) 54%; (b) 240