Reggie, Ahmad and Lee had some cards in the ratio of 4 : 5 : 9. Lee gave 40% of his cards to Reggie and Ahmad. As a result, Reggie had the same number of cards as Ahmad and Lee had 18 fewer cards than Reggie.

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

Reggie	Ahmad	Lee	Total
4 u	5 u	9 u	18 u
+ 3.6 u		- 3.6 u
6.3 u	6.3 u	5.4 u	18 u

(a)
Number of cards that Lee gave away
= 40% x 9
= ⁴⁰₁₀₀ x 9
= 3.6 u

Number of cards that Reggie and Ahmad each had in the end
= (18 u - 5.4 u) ÷ 2
= 12.6 u ÷ 2
= 6.3 u

Increase in the number of cards that Reggie had
= 6.3 u - 4 u
= 2.3 u

Percentage increase in Reggie's cards after receiving from Lee
= ^2.3₄ x 100%
= 57.5%

(b)
6.3 u = 5.4 u + 18
6.3 u - 5.4 u = 18
0.9 u = 18

1 u = 18 ÷ 0.9 = 20

Number of cards that Ahmad had at first
= 5 u
= 5 x 20
= 100

Answer(s): (a) 57.5%; (b) 100