Henry, Cody and Sean had some beads in the ratio of 4 : 5 : 9. Sean gave 50% of his beads to Henry and Cody. As a result, Henry had the same number of beads as Cody and Sean had 36 fewer beads than Henry.

1. What was the percentage increase in Henry's beads after receiving from Sean?
2. How many beads did Cody have at first?

Henry	Cody	Sean	Total
4 u	5 u	9 u	18 u
+ 4.5 u		- 4.5 u
6.75 u	6.75 u	4.5 u	18 u

(a)
Number of beads that Sean gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of beads that Henry and Cody each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of beads that Henry had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Henry's beads after receiving from Sean
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 36
6.75 u - 4.5 u = 36
2.25 u = 36

1 u = 36 ÷ 2.25 = 16

Number of beads that Cody had at first
= 5 u
= 5 x 16
= 80

Answer(s): (a) 68.75%; (b) 80