Xavier, Cody and Sean had some coins in the ratio of 2 : 3 : 5. Sean gave 50% of his coins to Xavier and Cody. As a result, Xavier had the same number of coins as Cody and Sean had 40 fewer coins than Xavier.

1. What was the percentage increase in Xavier's coins after receiving from Sean?
2. How many coins did Cody have at first?

Xavier	Cody	Sean	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 coins that Sean gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of coins that Xavier and Cody each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of coins that Xavier had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Xavier's coins after receiving from Sean
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of coins that Cody had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96