Peter, Sam and Howard had some stickers in the ratio of 2 : 3 : 5. Howard gave 40% of his stickers to Peter and Sam. As a result, Peter had the same number of stickers as Sam and Howard had 33 fewer stickers than Peter.

1. What was the percentage increase in Peter's stickers after receiving from Howard?
2. How many stickers did Sam have at first?

Peter	Sam	Howard	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of stickers that Howard gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of stickers that Peter and Sam each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of stickers that Peter had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Peter's stickers after receiving from Howard
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 33
3.5 u - 3 u = 33
0.5 u = 33

1 u = 33 ÷ 0.5 = 66

Number of stickers that Sam had at first
= 3 u
= 3 x 66
= 198

Answer(s): (a) 75%; (b) 198