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

1. What was the percentage increase in Pierre's pens after receiving from Jeremy?
2. How many pens did Riordan have at first?

Pierre	Riordan	Jeremy	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 Jeremy gave away
= 50% x 13
= ⁵⁰₁₀₀ x 13
= 6.5 u

Number of pens that Pierre and Riordan 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 Pierre had
= 9.75 u - 6 u
= 3.75 u

Percentage increase in Pierre's pens after receiving from Jeremy
= ^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 Riordan had at first
= 7 u
= 7 x 12
= 84

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