Ivan, Henry and Xavier had some buttons in the ratio of 2 : 3 : 5. Xavier gave 40% of his buttons to Ivan and Henry. As a result, Ivan had the same number of buttons as Henry and Xavier had 49 fewer buttons than Ivan.

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

Ivan	Henry	Xavier	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 Xavier gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 49
3.5 u - 3 u = 49
0.5 u = 49

1 u = 49 ÷ 0.5 = 98

Number of buttons that Henry had at first
= 3 u
= 3 x 98
= 294

Answer(s): (a) 75%; (b) 294