Reggie, Liam and Mark had some cards in the ratio of 2 : 3 : 5. Mark gave 50% of his cards to Reggie and Liam. As a result, Reggie had the same number of cards as Liam and Mark had 50 fewer cards than Reggie.

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

Reggie	Liam	Mark	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 Mark gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that Reggie and Liam 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 Reggie had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 50
3.75 u - 2.5 u = 50
1.25 u = 50

1 u = 50 ÷ 1.25 = 40

Number of cards that Liam had at first
= 3 u
= 3 x 40
= 120

Answer(s): (a) 87.5%; (b) 120