Liam, Cody and Tom had some buttons in the ratio of 3 : 4 : 7. Tom gave 40% of his buttons to Liam and Cody. As a result, Liam had the same number of buttons as Cody and Tom had 14 fewer buttons than Liam.

1. What was the percentage increase in Liam's buttons after receiving from Tom?
2. How many buttons did Cody have at first?

Liam	Cody	Tom	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 Tom gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of buttons that Liam and Cody 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 Liam had
= 4.9 u - 3 u
= 1.9 u

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

(b)
4.9 u = 4.2 u + 14
4.9 u - 4.2 u = 14
0.7 u = 14

1 u = 14 ÷ 0.7 = 20

Number of buttons that Cody had at first
= 4 u
= 4 x 20
= 80

Answer(s): (a) 63.333333333333%; (b) 80