Japheth, Howard and Jeremy had some erasers in the ratio of 3 : 4 : 7. Jeremy gave 40% of his erasers to Japheth and Howard. As a result, Japheth had the same number of erasers as Howard and Jeremy had 14 fewer erasers than Japheth.

1. What was the percentage increase in Japheth's erasers after receiving from Jeremy?
2. How many erasers did Howard have at first?

Japheth	Howard	Jeremy	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 Jeremy gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of erasers that Japheth and Howard 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 Japheth had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Japheth's erasers after receiving from Jeremy
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 14
4.9 u - 4.2 u = 14
0.7 u = 14

1 u = 14 ÷ 0.7 = 20

Number of erasers that Howard had at first
= 4 u
= 4 x 20
= 80

Answer(s): (a) 63.333333333333%; (b) 80