Tommy, Jenson and George had some buttons in the ratio of 3 : 4 : 7. George gave 40% of his buttons to Tommy and Jenson. As a result, Tommy had the same number of buttons as Jenson and George had 35 fewer buttons than Tommy.

1. What was the percentage increase in Tommy's buttons after receiving from George?
2. How many buttons did Jenson have at first?

Tommy	Jenson	George	Total
3 u	4 u	7 u	14 u
+ 2.8 u		- 2.8 u
4.9 u	4.9 u	4.2 u	14 u

(a)
Number of buttons that George gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of buttons that Tommy and Jenson each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of buttons that Tommy had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Tommy's buttons after receiving from George
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 35
4.9 u - 4.2 u = 35
0.7 u = 35

1 u = 35 ÷ 0.7 = 50

Number of buttons that Jenson had at first
= 4 u
= 4 x 50
= 200

Answer(s): (a) 63.333333333333%; (b) 200