Luis, Japheth and Tim had some erasers in the ratio of 6 : 7 : 13. Tim gave 50% of his erasers to Luis and Japheth. As a result, Luis had the same number of erasers as Japheth and Tim had 26 fewer erasers than Luis.

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

Luis	Japheth	Tim	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 erasers that Tim gave away
= 50% x 13
= ⁵⁰₁₀₀ x 13
= 6.5 u

Number of erasers that Luis and Japheth each had in the end
= (26 u - 6.5 u) ÷ 2
= 19.5 u ÷ 2
= 9.75 u

Increase in the number of erasers that Luis had
= 9.75 u - 6 u
= 3.75 u

Percentage increase in Luis's erasers after receiving from Tim
= ^3.75₆ x 100%
= 62.5%

(b)
9.75 u = 6.5 u + 26
9.75 u - 6.5 u = 26
3.25 u = 26

1 u = 26 ÷ 3.25 = 8

Number of erasers that Japheth had at first
= 7 u
= 7 x 8
= 56

Answer(s): (a) 62.5%; (b) 56