Wendy and Lucy had a total of 126 marbles. Lucy gave ¹₄ of her marbles to Wendy. In return, Wendy gave ¹₈ of the total number of marbles that she had to Lucy. In the end, each girl had the same number of marbles. How many marbles did Wendy have at first?

	Wendy	Lucy	Total
Before 1	?	4 u	126
Change 1	+ 1 u	- 1 u
After 1	72	3 u	126
Before 2	8 p	3 u	126
Change 2	- 1 p	+ 1 p
After 2	7 p (63)	63	126

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

Number of marbles that Lucy and Wendy each had in the end is the same.

Number of marbles that Wendy had in the end
= 126 ÷ 2
= 63

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

7 p = 63

1 p = 63 ÷ 7 = 9

Number of marbles that Wendy had after receiving some marbles from Lucy
= 8 p
= 8 x 9
= 72

Number of marbles that Lucy had after giving to Wendy
= 126 - 72
= 54

3 u = 54

1 u = 54 ÷ 3 = 18

Number of marbles that Lucy had at first
= 4 u
= 4 x 18
= 72

Number of marbles that Wendy had at first
= 126 - 72
= 54

Answer(s): 54