Dylan, Fred and Zane had some coins in the ratio of 3 : 4 : 7. Zane gave 50% of his coins to Dylan and Fred. As a result, Dylan had the same number of coins as Fred and Zane had 14 fewer coins than Dylan.

1. What was the percentage increase in Dylan's coins after receiving from Zane?
2. How many coins did Fred have at first?

Dylan	Fred	Zane	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 Zane gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of coins that Dylan and Fred 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 Dylan had
= 5.25 u - 3 u
= 2.25 u

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

(b)
5.25 u = 3.5 u + 14
5.25 u - 3.5 u = 14
1.75 u = 14

1 u = 14 ÷ 1.75 = 8

Number of coins that Fred had at first
= 4 u
= 4 x 8
= 32

Answer(s): (a) 75%; (b) 32