Caden, Will and George had some coins in the ratio of 3 : 4 : 7. George gave 50% of his coins to Caden and Will. As a result, Caden had the same number of coins as Will and George had 49 fewer coins than Caden.

1. What was the percentage increase in Caden's coins after receiving from George?
2. How many coins did Will have at first?

Caden	Will	George	Total
3 u	4 u	7 u	14 u
+ 3.5 u		- 3.5 u
5.25 u	5.25 u	3.5 u	14 u

(a)
Number of coins that George gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of coins that Caden and Will each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u

Increase in the number of coins that Caden had
= 5.25 u - 3 u
= 2.25 u

Percentage increase in Caden's coins after receiving from George
= ^2.25₃ x 100%
= 75%

(b)
5.25 u = 3.5 u + 49
5.25 u - 3.5 u = 49
1.75 u = 49

1 u = 49 ÷ 1.75 = 28

Number of coins that Will had at first
= 4 u
= 4 x 28
= 112

Answer(s): (a) 75%; (b) 112