Betty and Joelle had a total of 20 erasers. Joelle gave ¹₃ of her erasers to Betty. In return, Betty gave ¹₆ of the total number of erasers that she had to Joelle. In the end, each girl had the same number of erasers. How many erasers did Betty have at first?

	Betty	Joelle	Total
Before 1	?	3 u	20
Change 1	+ 1 u	- 1 u
After 1	12	2 u	20
Before 2	6 p	2 u	20
Change 2	- 1 p	+ 1 p
After 2	5 p (10)	10	20

Since Joelle gave some erasers to Betty and Betty then gave some erasers to Joelle, it is an internal transfer of erasers between the two girls. So, the total number of erasers remains unchanged.

Number of erasers that Joelle and Betty each had in the end is the same.

Number of erasers that Betty had in the end
= 20 ÷ 2
= 10

Number of erasers that Betty had in the end = 5 p

5 p = 10

1 p = 10 ÷ 5 = 2

Number of erasers that Betty had after receiving some erasers from Joelle
= 6 p
= 6 x 2
= 12

Number of erasers that Joelle had after giving to Betty
= 20 - 12
= 8

2 u = 8

1 u = 8 ÷ 2 = 4

Number of erasers that Joelle had at first
= 3 u
= 3 x 4
= 12

Number of erasers that Betty had at first
= 20 - 12
= 8

Answer(s): 8