Cole, Japheth and Wesley had some buttons in the ratio of 2 : 3 : 5. Wesley gave 40% of his buttons to Cole and Japheth. As a result, Cole had the same number of buttons as Japheth and Wesley had 47 fewer buttons than Cole.

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

Cole	Japheth	Wesley	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 Wesley gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 47
3.5 u - 3 u = 47
0.5 u = 47

1 u = 47 ÷ 0.5 = 94

Number of buttons that Japheth had at first
= 3 u
= 3 x 94
= 282

Answer(s): (a) 75%; (b) 282