Reggie, Howard and Lee had some coins in the ratio of 6 : 7 : 13. Lee gave 40% of his coins to Reggie and Howard. As a result, Reggie had the same number of coins as Howard and Lee had 26 fewer coins than Reggie.

1. What was the percentage increase in Reggie's coins after receiving from Lee?
2. How many coins did Howard have at first?

Reggie	Howard	Lee	Total
6 u	7 u	13 u	26 u
+ 5.2 u		- 5.2 u
9.1 u	9.1 u	7.8 u	26 u

(a)
Number of coins that Lee gave away
= 40% x 13
= ⁴⁰₁₀₀ x 13
= 5.2 u

Number of coins that Reggie and Howard each had in the end
= (26 u - 7.8 u) ÷ 2
= 18.2 u ÷ 2
= 9.1 u

Increase in the number of coins that Reggie had
= 9.1 u - 6 u
= 3.1 u

Percentage increase in Reggie's coins after receiving from Lee
= ^3.1₆ x 100%
= 51.666666666667%

(b)
9.1 u = 7.8 u + 26
9.1 u - 7.8 u = 26
1.3 u = 26

1 u = 26 ÷ 1.3 = 20

Number of coins that Howard had at first
= 7 u
= 7 x 20
= 140

Answer(s): (a) 51.666666666667%; (b) 140