David, Reggie and Paul had some marbles in the ratio of 6 : 7 : 13. Paul gave 40% of his marbles to David and Reggie. As a result, David had the same number of marbles as Reggie and Paul had 13 fewer marbles than David.

1. What was the percentage increase in David's marbles after receiving from Paul?
2. How many marbles did Reggie have at first?

David	Reggie	Paul	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 marbles that Paul gave away
= 40% x 13
= ⁴⁰₁₀₀ x 13
= 5.2 u

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

Increase in the number of marbles that David had
= 9.1 u - 6 u
= 3.1 u

Percentage increase in David's marbles after receiving from Paul
= ^3.1₆ x 100%
= 51.666666666667%

(b)
9.1 u = 7.8 u + 13
9.1 u - 7.8 u = 13
1.3 u = 13

1 u = 13 ÷ 1.3 = 10

Number of marbles that Reggie had at first
= 7 u
= 7 x 10
= 70

Answer(s): (a) 51.666666666667%; (b) 70