Gwen had some pomegranates and oranges in 2 baskets. In Basket J, the number of pomegranates to the number of oranges was in the ratio of 2 : 9. In Basket K, there were four times as many pomegranates as oranges. After Gwen transferred ¹₃ of the oranges from Basket J to Basket K, the number of fruits left in Basket J was 208 and the ratio of the number of pomegranates to the number of oranges in Basket B became 3 : 4. How many fruits were in Basket K in the end?

	Basket J		Basket K
	Pomegranates	Oranges	Pomegranates	Oranges
Before	2 u	9 u	4x3 =  12 p	1x3 = 3 p
Change		- 3 u		+ 3 u (+ 13 p)
After	2 u	6 u	3x4 = 12 p	4x4 = 16 p

Number of oranges that Gwen transferred from Basket J to Basket K
= ¹₃ x 9 u
= 3 u

Total number of fruits in Basket J in the end
= 2 u + 6 u
= 8 u

8 u = 208
1 u = 208 ÷ 8 = 26

The number of pomegranates in Basket K is the unchanged quantity.
LCM of 4 and 3 is 12.

Number of oranges that Gwen transferred from Basket J to Basket K
= 3 u
= 3 x 26
= 78

Increase in the number of oranges that due to the transfer from Basket J to Basket K
= 16 p - 3 p
= 13 p

13 p = 3 u 
13 p = 78

1 p = 78 ÷ 13 = 6

Number of fruits in Basket K in the end
= 12 p + 16 p
= 28 p
= 28 x 6
= 168

Answer(s): 168