Xavier, Howard and Luke had some stamps in the ratio of 3 : 4 : 7. Luke gave 40% of his stamps to Xavier and Howard. As a result, Xavier had the same number of stamps as Howard and Luke had 14 fewer stamps than Xavier.

1. What was the percentage increase in Xavier's stamps after receiving from Luke?
2. How many stamps did Howard have at first?

Xavier	Howard	Luke	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 stamps that Luke gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of stamps that Xavier and Howard each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of stamps that Xavier had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Xavier's stamps after receiving from Luke
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 14
4.9 u - 4.2 u = 14
0.7 u = 14

1 u = 14 ÷ 0.7 = 20

Number of stamps that Howard had at first
= 4 u
= 4 x 20
= 80

Answer(s): (a) 63.333333333333%; (b) 80