Marion and Tammy had a total of 36 marbles. Tammy gave ¹₅ of her marbles to Marion. In return, Marion gave ¹₄ of the total number of marbles that she had to Tammy. In the end, each girl had the same number of marbles. How many marbles did Marion have at first?

	Marion	Tammy	Total
Before 1	?	5 u	36
Change 1	+ 1 u	- 1 u
After 1	24	4 u	36
Before 2	4 p	4 u	36
Change 2	- 1 p	+ 1 p
After 2	3 p (18)	18	36

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

Number of marbles that Tammy and Marion each had in the end is the same.

Number of marbles that Marion had in the end
= 36 ÷ 2
= 18

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

3 p = 18

1 p = 18 ÷ 3 = 6

Number of marbles that Marion had after receiving some marbles from Tammy
= 4 p
= 4 x 6
= 24

Number of marbles that Tammy had after giving to Marion
= 36 - 24
= 12

4 u = 12

1 u = 12 ÷ 4 = 3

Number of marbles that Tammy had at first
= 5 u
= 5 x 3
= 15

Number of marbles that Marion had at first
= 36 - 15
= 21

Answer(s): 21