Opal and Rachel had a total of 60 marbles. Rachel gave ¹₆ of her marbles to Opal. In return, Opal gave ¹₄ of the total number of marbles that she had to Rachel. In the end, each girl had the same number of marbles. How many marbles did Opal have at first?

	Opal	Rachel	Total
Before 1	?	6 u	60
Change 1	+ 1 u	- 1 u
After 1	40	5 u	60
Before 2	4 p	5 u	60
Change 2	- 1 p	+ 1 p
After 2	3 p (30)	30	60

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

Number of marbles that Rachel and Opal each had in the end is the same.

Number of marbles that Opal had in the end
= 60 ÷ 2
= 30

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

3 p = 30

1 p = 30 ÷ 3 = 10

Number of marbles that Opal had after receiving some marbles from Rachel
= 4 p
= 4 x 10
= 40

Number of marbles that Rachel had after giving to Opal
= 60 - 40
= 20

5 u = 20

1 u = 20 ÷ 5 = 4

Number of marbles that Rachel had at first
= 6 u
= 6 x 4
= 24

Number of marbles that Opal had at first
= 60 - 24
= 36

Answer(s): 36