Carl, Gabriel and Fred had some pens in the ratio of 3 : 4 : 7. Fred gave 40% of his pens to Carl and Gabriel. As a result, Carl had the same number of pens as Gabriel and Fred had 49 fewer pens than Carl.

1. What was the percentage increase in Carl's pens after receiving from Fred?
2. How many pens did Gabriel have at first?

Carl	Gabriel	Fred	Total
3 u	4 u	7 u	14 u
+ 2.8 u		- 2.8 u
4.9 u	4.9 u	4.2 u	14 u

(a)
Number of pens that Fred gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of pens that Carl and Gabriel each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of pens that Carl had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Carl's pens after receiving from Fred
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 49
4.9 u - 4.2 u = 49
0.7 u = 49

1 u = 49 ÷ 0.7 = 70

Number of pens that Gabriel had at first
= 4 u
= 4 x 70
= 280

Answer(s): (a) 63.333333333333%; (b) 280