Julian, Caden and Tom had some pens in the ratio of 4 : 5 : 9. Tom gave 50% of his pens to Julian and Caden. As a result, Julian had the same number of pens as Caden and Tom had 27 fewer pens than Julian.

1. What was the percentage increase in Julian's pens after receiving from Tom?
2. How many pens did Caden have at first?

Julian	Caden	Tom	Total
4 u	5 u	9 u	18 u
+ 4.5 u		- 4.5 u
6.75 u	6.75 u	4.5 u	18 u

(a)
Number of pens that Tom gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of pens that Julian and Caden each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of pens that Julian had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Julian's pens after receiving from Tom
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 27
6.75 u - 4.5 u = 27
2.25 u = 27

1 u = 27 ÷ 2.25 = 12

Number of pens that Caden had at first
= 5 u
= 5 x 12
= 60

Answer(s): (a) 68.75%; (b) 60