Ken, Andy and Luke had some stamps in the ratio of 6 : 7 : 13. Luke gave 50% of his stamps to Ken and Andy. As a result, Ken had the same number of stamps as Andy and Luke had 13 fewer stamps than Ken.

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

Ken	Andy	Luke	Total
6 u	7 u	13 u	26 u
+ 6.5 u		- 6.5 u
9.75 u	9.75 u	6.5 u	26 u

(a)
Number of stamps that Luke gave away
= 50% x 13
= ⁵⁰₁₀₀ x 13
= 6.5 u

Number of stamps that Ken and Andy each had in the end
= (26 u - 6.5 u) ÷ 2
= 19.5 u ÷ 2
= 9.75 u

Increase in the number of stamps that Ken had
= 9.75 u - 6 u
= 3.75 u

Percentage increase in Ken's stamps after receiving from Luke
= ^3.75₆ x 100%
= 62.5%

(b)
9.75 u = 6.5 u + 13
9.75 u - 6.5 u = 13
3.25 u = 13

1 u = 13 ÷ 3.25 = 4

Number of stamps that Andy had at first
= 7 u
= 7 x 4
= 28

Answer(s): (a) 62.5%; (b) 28