Seth, Charlie and Jenson had some pens in the ratio of 6 : 7 : 13. Jenson gave 50% of his pens to Seth and Charlie. As a result, Seth had the same number of pens as Charlie and Jenson had 39 fewer pens than Seth.

1. What was the percentage increase in Seth's pens after receiving from Jenson?
2. How many pens did Charlie have at first?

Seth	Charlie	Jenson	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 pens that Jenson gave away
= 50% x 13
= ⁵⁰₁₀₀ x 13
= 6.5 u

Number of pens that Seth and Charlie each had in the end
= (26 u - 6.5 u) ÷ 2
= 19.5 u ÷ 2
= 9.75 u

Increase in the number of pens that Seth had
= 9.75 u - 6 u
= 3.75 u

Percentage increase in Seth's pens after receiving from Jenson
= ^3.75₆ x 100%
= 62.5%

(b)
9.75 u = 6.5 u + 39
9.75 u - 6.5 u = 39
3.25 u = 39

1 u = 39 ÷ 3.25 = 12

Number of pens that Charlie had at first
= 7 u
= 7 x 12
= 84

Answer(s): (a) 62.5%; (b) 84