Harry, Howard and Lee had some marbles in the ratio of 4 : 5 : 9. Lee gave 40% of his marbles to Harry and Howard. As a result, Harry had the same number of marbles as Howard and Lee had 18 fewer marbles than Harry.

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

Harry	Howard	Lee	Total
4 u	5 u	9 u	18 u
+ 3.6 u		- 3.6 u
6.3 u	6.3 u	5.4 u	18 u

(a)
Number of marbles that Lee gave away
= 40% x 9
= ⁴⁰₁₀₀ x 9
= 3.6 u

Number of marbles that Harry and Howard each had in the end
= (18 u - 5.4 u) ÷ 2
= 12.6 u ÷ 2
= 6.3 u

Increase in the number of marbles that Harry had
= 6.3 u - 4 u
= 2.3 u

Percentage increase in Harry's marbles after receiving from Lee
= ^2.3₄ x 100%
= 57.5%

(b)
6.3 u = 5.4 u + 18
6.3 u - 5.4 u = 18
0.9 u = 18

1 u = 18 ÷ 0.9 = 20

Number of marbles that Howard had at first
= 5 u
= 5 x 20
= 100

Answer(s): (a) 57.5%; (b) 100