Fred, Jeremy and Owen had some cards in the ratio of 2 : 3 : 5. Owen gave 50% of his cards to Fred and Jeremy. As a result, Fred had the same number of cards as Jeremy and Owen had 35 fewer cards than Fred.

1. What was the percentage increase in Fred's cards after receiving from Owen?
2. How many cards did Jeremy have at first?

Fred	Jeremy	Owen	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 Owen gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that Fred and Jeremy 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 Fred had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 35
3.75 u - 2.5 u = 35
1.25 u = 35

1 u = 35 ÷ 1.25 = 28

Number of cards that Jeremy had at first
= 3 u
= 3 x 28
= 84

Answer(s): (a) 87.5%; (b) 84