Jen and Abi had a total of 144 marbles. Abi gave ¹₃ of her marbles to Jen. In return, Jen gave ¹₇ of the total number of marbles that she had to Abi. In the end, each girl had the same number of marbles. How many marbles did Jen have at first?

	Jen	Abi	Total
Before 1	?	3 u	144
Change 1	+ 1 u	- 1 u
After 1	84	2 u	144
Before 2	7 p	2 u	144
Change 2	- 1 p	+ 1 p
After 2	6 p (72)	72	144

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

Number of marbles that Abi and Jen each had in the end is the same.

Number of marbles that Jen had in the end
= 144 ÷ 2
= 72

Number of marbles that Jen had in the end = 6 p

6 p = 72

1 p = 72 ÷ 6 = 12

Number of marbles that Jen had after receiving some marbles from Abi
= 7 p
= 7 x 12
= 84

Number of marbles that Abi had after giving to Jen
= 144 - 84
= 60

2 u = 60

1 u = 60 ÷ 2 = 30

Number of marbles that Abi had at first
= 3 u
= 3 x 30
= 90

Number of marbles that Jen had at first
= 144 - 90
= 54

Answer(s): 54