Tom, Glen and Albert had some erasers in the ratio of 3 : 4 : 7. Albert gave 50% of his erasers to Tom and Glen. As a result, Tom had the same number of erasers as Glen and Albert had 42 fewer erasers than Tom.

1. What was the percentage increase in Tom's erasers after receiving from Albert?
2. How many erasers did Glen have at first?

Tom	Glen	Albert	Total
3 u	4 u	7 u	14 u
+ 3.5 u		- 3.5 u
5.25 u	5.25 u	3.5 u	14 u

(a)
Number of erasers that Albert gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of erasers that Tom and Glen each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u

Increase in the number of erasers that Tom had
= 5.25 u - 3 u
= 2.25 u

Percentage increase in Tom's erasers after receiving from Albert
= ^2.25₃ x 100%
= 75%

(b)
5.25 u = 3.5 u + 42
5.25 u - 3.5 u = 42
1.75 u = 42

1 u = 42 ÷ 1.75 = 24

Number of erasers that Glen had at first
= 4 u
= 4 x 24
= 96

Answer(s): (a) 75%; (b) 96