Tammy had some pears and persimmons in 2 baskets. In Basket W, the number of pears to the number of persimmons was in the ratio of 5 : 9. In Basket X, there were thrice as many pears as persimmons. After Tammy transferred ¹₃ of the persimmons from Basket W to Basket X, the number of fruits left in Basket W was 165 and the ratio of the number of pears to the number of persimmons in Basket B became 6 : 7. How many fruits were in Basket X in the end?

	Basket W		Basket X
	Pears	Persimmons	Pears	Persimmons
Before	5 u	9 u	3x2 =  6 p	1x2 = 2 p
Change		- 3 u		+ 3 u (+ 5 p)
After	5 u	6 u	6x1 = 6 p	7x1 = 7 p

Number of persimmons that Tammy transferred from Basket W to Basket X
= ¹₃ x 9 u
= 3 u

Total number of fruits in Basket W in the end
= 5 u + 6 u
= 11 u

11 u = 165
1 u = 165 ÷ 11 = 15

The number of pears in Basket X is the unchanged quantity.
LCM of 3 and 6 is 6.

Number of persimmons that Tammy transferred from Basket W to Basket X
= 3 u
= 3 x 15
= 45

Increase in the number of persimmons that due to the transfer from Basket W to Basket X
= 7 p - 2 p
= 5 p

5 p = 3 u 
5 p = 45

1 p = 45 ÷ 5 = 9

Number of fruits in Basket X in the end
= 6 p + 7 p
= 13 p
= 13 x 9
= 117

Answer(s): 117