Howard, Tom and Brandon had some erasers in the ratio of 5 : 6 : 11. Brandon gave 50% of his erasers to Howard and Tom. As a result, Howard had the same number of erasers as Tom and Brandon had 33 fewer erasers than Howard.

1. What was the percentage increase in Howard's erasers after receiving from Brandon?
2. How many erasers did Tom have at first?

Howard	Tom	Brandon	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of erasers that Brandon gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of erasers that Howard and Tom each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of erasers that Howard had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Howard's erasers after receiving from Brandon
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 33
8.25 u - 5.5 u = 33
2.75 u = 33

1 u = 33 ÷ 2.75 = 12

Number of erasers that Tom had at first
= 6 u
= 6 x 12
= 72

Answer(s): (a) 65%; (b) 72