Xavier, Cole and Jack had some buttons in the ratio of 2 : 3 : 5. Jack gave 40% of his buttons to Xavier and Cole. As a result, Xavier had the same number of buttons as Cole and Jack had 36 fewer buttons than Xavier.

1. What was the percentage increase in Xavier's buttons after receiving from Jack?
2. How many buttons did Cole have at first?

Xavier	Cole	Jack	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of buttons that Jack gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of buttons that Xavier and Cole each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of buttons that Xavier had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Xavier's buttons after receiving from Jack
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 36
3.5 u - 3 u = 36
0.5 u = 36

1 u = 36 ÷ 0.5 = 72

Number of buttons that Cole had at first
= 3 u
= 3 x 72
= 216

Answer(s): (a) 75%; (b) 216