Ethan, Luke and Albert had some beads in the ratio of 3 : 4 : 7. Albert gave 50% of his beads to Ethan and Luke. As a result, Ethan had the same number of beads as Luke and Albert had 49 fewer beads than Ethan.

1. What was the percentage increase in Ethan's beads after receiving from Albert?
2. How many beads did Luke have at first?

Ethan	Luke	Albert	Total
3 u	4 u	7 u	14 u
+ 3.5 u		- 3.5 u
5.25 u	5.25 u	3.5 u	14 u

(a)
Number of beads that Albert gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of beads that Ethan and Luke each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u

Increase in the number of beads that Ethan had
= 5.25 u - 3 u
= 2.25 u

Percentage increase in Ethan's beads after receiving from Albert
= ^2.25₃ x 100%
= 75%

(b)
5.25 u = 3.5 u + 49
5.25 u - 3.5 u = 49
1.75 u = 49

1 u = 49 ÷ 1.75 = 28

Number of beads that Luke had at first
= 4 u
= 4 x 28
= 112

Answer(s): (a) 75%; (b) 112