Marion and Xylia had a total of 72 erasers. Xylia gave ¹₅ of her erasers to Marion. In return, Marion gave ¹₄ of the total number of erasers that she had to Xylia. In the end, each girl had the same number of erasers. How many erasers did Marion have at first?

	Marion	Xylia	Total
Before 1	?	5 u	72
Change 1	+ 1 u	- 1 u
After 1	48	4 u	72
Before 2	4 p	4 u	72
Change 2	- 1 p	+ 1 p
After 2	3 p (36)	36	72

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

Number of erasers that Xylia and Marion each had in the end is the same.

Number of erasers that Marion had in the end
= 72 ÷ 2
= 36

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

3 p = 36

1 p = 36 ÷ 3 = 12

Number of erasers that Marion had after receiving some erasers from Xylia
= 4 p
= 4 x 12
= 48

Number of erasers that Xylia had after giving to Marion
= 72 - 48
= 24

4 u = 24

1 u = 24 ÷ 4 = 6

Number of erasers that Xylia had at first
= 5 u
= 5 x 6
= 30

Number of erasers that Marion had at first
= 72 - 30
= 42

Answer(s): 42