Ivory and Diana had a total of 36 pens. Diana gave ¹₄ of her pens to Ivory. In return, Ivory gave ¹₃ of the total number of pens that she had to Diana. In the end, each girl had the same number of pens. How many pens did Ivory have at first?

	Ivory	Diana	Total
Before 1	?	4 u	36
Change 1	+ 1 u	- 1 u
After 1	27	3 u	36
Before 2	3 p	3 u	36
Change 2	- 1 p	+ 1 p
After 2	2 p (18)	18	36

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

Number of pens that Diana and Ivory each had in the end is the same.

Number of pens that Ivory had in the end
= 36 ÷ 2
= 18

Number of pens that Ivory had in the end = 2 p

2 p = 18

1 p = 18 ÷ 2 = 9

Number of pens that Ivory had after receiving some pens from Diana
= 3 p
= 3 x 9
= 27

Number of pens that Diana had after giving to Ivory
= 36 - 27
= 9

3 u = 9

1 u = 9 ÷ 3 = 3

Number of pens that Diana had at first
= 4 u
= 4 x 3
= 12

Number of pens that Ivory had at first
= 36 - 12
= 24

Answer(s): 24