Ivan, Ryan and Julian had some beads in the ratio of 3 : 4 : 7. Julian gave 40% of his beads to Ivan and Ryan. As a result, Ivan had the same number of beads as Ryan and Julian had 42 fewer beads than Ivan.

1. What was the percentage increase in Ivan's beads after receiving from Julian?
2. How many beads did Ryan have at first?

Ivan	Ryan	Julian	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 beads that Julian gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of beads that Ivan and Ryan each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of beads that Ivan had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Ivan's beads after receiving from Julian
= ^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 beads that Ryan had at first
= 4 u
= 4 x 60
= 240

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