Elijah, Justin and Glen had some beads in the ratio of 3 : 4 : 7. Glen gave 40% of his beads to Elijah and Justin. As a result, Elijah had the same number of beads as Justin and Glen had 28 fewer beads than Elijah.

1. What was the percentage increase in Elijah's beads after receiving from Glen?
2. How many beads did Justin have at first?

Elijah	Justin	Glen	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 Glen gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of beads that Elijah and Justin 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 Elijah had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Elijah's beads after receiving from Glen
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 28
4.9 u - 4.2 u = 28
0.7 u = 28

1 u = 28 ÷ 0.7 = 40

Number of beads that Justin had at first
= 4 u
= 4 x 40
= 160

Answer(s): (a) 63.333333333333%; (b) 160