Emma and Mary had a total of 126 pens. Mary gave ¹₃ of her pens to Emma. In return, Emma gave ¹₈ of the total number of pens that she had to Mary. In the end, each girl had the same number of pens. How many pens did Emma have at first?

	Emma	Mary	Total
Before 1	?	3 u	126
Change 1	+ 1 u	- 1 u
After 1	72	2 u	126
Before 2	8 p	2 u	126
Change 2	- 1 p	+ 1 p
After 2	7 p (63)	63	126

Since Mary gave some pens to Emma and Emma then gave some pens to Mary, it is an internal transfer of pens between the two girls. So, the total number of pens remains unchanged.

Number of pens that Mary and Emma each had in the end is the same.

Number of pens that Emma had in the end
= 126 ÷ 2
= 63

Number of pens that Emma had in the end = 7 p

7 p = 63

1 p = 63 ÷ 7 = 9

Number of pens that Emma had after receiving some pens from Mary
= 8 p
= 8 x 9
= 72

Number of pens that Mary had after giving to Emma
= 126 - 72
= 54

2 u = 54

1 u = 54 ÷ 2 = 27

Number of pens that Mary had at first
= 3 u
= 3 x 27
= 81

Number of pens that Emma had at first
= 126 - 81
= 45

Answer(s): 45