Elijah, Peter and Michael had some cards in the ratio of 2 : 3 : 5. Michael gave 50% of his cards to Elijah and Peter. As a result, Elijah had the same number of cards as Peter and Michael had 10 fewer cards than Elijah.

1. What was the percentage increase in Elijah's cards after receiving from Michael?
2. How many cards did Peter have at first?

Elijah	Peter	Michael	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 Michael gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that Elijah and Peter 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 Elijah had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 10
3.75 u - 2.5 u = 10
1.25 u = 10

1 u = 10 ÷ 1.25 = 8

Number of cards that Peter had at first
= 3 u
= 3 x 8
= 24

Answer(s): (a) 87.5%; (b) 24