Luke, Neave and Fabian had some pens in the ratio of 5 : 6 : 11. Fabian gave 50% of his pens to Luke and Neave. As a result, Luke had the same number of pens as Neave and Fabian had 11 fewer pens than Luke.

1. What was the percentage increase in Luke's pens after receiving from Fabian?
2. How many pens did Neave have at first?

Luke	Neave	Fabian	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 pens that Fabian gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of pens that Luke and Neave each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of pens that Luke had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Luke's pens after receiving from Fabian
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 11
8.25 u - 5.5 u = 11
2.75 u = 11

1 u = 11 ÷ 2.75 = 4

Number of pens that Neave had at first
= 6 u
= 6 x 4
= 24

Answer(s): (a) 65%; (b) 24