Eva and Esther had a total of 168 marbles. Esther gave ¹₄ of her marbles to Eva. In return, Eva gave ¹₈ of the total number of marbles that she had to Esther. In the end, each girl had the same number of marbles. How many marbles did Eva have at first?

	Eva	Esther	Total
Before 1	?	4 u	168
Change 1	+ 1 u	- 1 u
After 1	96	3 u	168
Before 2	8 p	3 u	168
Change 2	- 1 p	+ 1 p
After 2	7 p (84)	84	168

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

Number of marbles that Esther and Eva each had in the end is the same.

Number of marbles that Eva had in the end
= 168 ÷ 2
= 84

Number of marbles that Eva had in the end = 7 p

7 p = 84

1 p = 84 ÷ 7 = 12

Number of marbles that Eva had after receiving some marbles from Esther
= 8 p
= 8 x 12
= 96

Number of marbles that Esther had after giving to Eva
= 168 - 96
= 72

3 u = 72

1 u = 72 ÷ 3 = 24

Number of marbles that Esther had at first
= 4 u
= 4 x 24
= 96

Number of marbles that Eva had at first
= 168 - 96
= 72

Answer(s): 72