Gillian and Olivia had a total of 60 erasers. Olivia gave ¹₅ of her erasers to Gillian. In return, Gillian gave ¹₄ of the total number of erasers that she had to Olivia. In the end, each girl had the same number of erasers. How many erasers did Gillian have at first?

	Gillian	Olivia	Total
Before 1	?	5 u	60
Change 1	+ 1 u	- 1 u
After 1	40	4 u	60
Before 2	4 p	4 u	60
Change 2	- 1 p	+ 1 p
After 2	3 p (30)	30	60

Since Olivia gave some erasers to Gillian and Gillian then gave some erasers to Olivia, it is an internal transfer of erasers between the two girls. So, the total number of erasers remains unchanged.

Number of erasers that Olivia and Gillian each had in the end is the same.

Number of erasers that Gillian had in the end
= 60 ÷ 2
= 30

Number of erasers that Gillian had in the end = 3 p

3 p = 30

1 p = 30 ÷ 3 = 10

Number of erasers that Gillian had after receiving some erasers from Olivia
= 4 p
= 4 x 10
= 40

Number of erasers that Olivia had after giving to Gillian
= 60 - 40
= 20

4 u = 20

1 u = 20 ÷ 4 = 5

Number of erasers that Olivia had at first
= 5 u
= 5 x 5
= 25

Number of erasers that Gillian had at first
= 60 - 25
= 35

Answer(s): 35