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

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

Fred	Caden	Gabriel	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 erasers that Gabriel gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of erasers that Fred and Caden each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of erasers that Fred had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Fred's erasers after receiving from Gabriel
= ^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 erasers that Caden had at first
= 4 u
= 4 x 70
= 280

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