Zeph, Perry and Billy had some marbles in the ratio of 3 : 4 : 7. Billy gave 40% of his marbles to Zeph and Perry. As a result, Zeph had the same number of marbles as Perry and Billy had 42 fewer marbles than Zeph.

1. What was the percentage increase in Zeph's marbles after receiving from Billy?
2. How many marbles did Perry have at first?

Zeph	Perry	Billy	Total
3 u	4 u	7 u	14 u
+ 2.8 u		- 2.8 u
4.9 u	4.9 u	4.2 u	14 u

(a)
Number of marbles that Billy gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of marbles that Zeph and Perry each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of marbles that Zeph had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Zeph's marbles after receiving from Billy
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 42
4.9 u - 4.2 u = 42
0.7 u = 42

1 u = 42 ÷ 0.7 = 60

Number of marbles that Perry had at first
= 4 u
= 4 x 60
= 240

Answer(s): (a) 63.333333333333%; (b) 240