Perry, Tommy and Caden had some buttons in the ratio of 6 : 7 : 13. Caden gave 50% of his buttons to Perry and Tommy. As a result, Perry had the same number of buttons as Tommy and Caden had 26 fewer buttons than Perry.

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

Perry	Tommy	Caden	Total
6 u	7 u	13 u	26 u
+ 6.5 u		- 6.5 u
9.75 u	9.75 u	6.5 u	26 u

(a)
Number of buttons that Caden gave away
= 50% x 13
= ⁵⁰₁₀₀ x 13
= 6.5 u

Number of buttons that Perry and Tommy each had in the end
= (26 u - 6.5 u) ÷ 2
= 19.5 u ÷ 2
= 9.75 u

Increase in the number of buttons that Perry had
= 9.75 u - 6 u
= 3.75 u

Percentage increase in Perry's buttons after receiving from Caden
= ^3.75₆ x 100%
= 62.5%

(b)
9.75 u = 6.5 u + 26
9.75 u - 6.5 u = 26
3.25 u = 26

1 u = 26 ÷ 3.25 = 8

Number of buttons that Tommy had at first
= 7 u
= 7 x 8
= 56

Answer(s): (a) 62.5%; (b) 56