Bobby, Valen and Henry had some marbles in the ratio of 2 : 3 : 5. Henry gave 40% of his marbles to Bobby and Valen. As a result, Bobby had the same number of marbles as Valen and Henry had 26 fewer marbles than Bobby.

1. What was the percentage increase in Bobby's marbles after receiving from Henry?
2. How many marbles did Valen have at first?

Bobby	Valen	Henry	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of marbles that Henry gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of marbles that Bobby and Valen each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of marbles that Bobby had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Bobby's marbles after receiving from Henry
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 26
3.5 u - 3 u = 26
0.5 u = 26

1 u = 26 ÷ 0.5 = 52

Number of marbles that Valen had at first
= 3 u
= 3 x 52
= 156

Answer(s): (a) 75%; (b) 156