Barbara and Usha had a total of 48 erasers. Usha gave ¹₃ of her erasers to Barbara. In return, Barbara gave ¹₅ of the total number of erasers that she had to Usha. In the end, each girl had the same number of erasers. How many erasers did Barbara have at first?

	Barbara	Usha	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	30	2 u	48
Before 2	5 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	4 p (24)	24	48

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

Number of erasers that Usha and Barbara each had in the end is the same.

Number of erasers that Barbara had in the end
= 48 ÷ 2
= 24

Number of erasers that Barbara had in the end = 4 p

4 p = 24

1 p = 24 ÷ 4 = 6

Number of erasers that Barbara had after receiving some erasers from Usha
= 5 p
= 5 x 6
= 30

Number of erasers that Usha had after giving to Barbara
= 48 - 30
= 18

2 u = 18

1 u = 18 ÷ 2 = 9

Number of erasers that Usha had at first
= 3 u
= 3 x 9
= 27

Number of erasers that Barbara had at first
= 48 - 27
= 21

Answer(s): 21