Sam had a total of 670 passion fruits and pomegranates. He sold ³₄ of the pomegranates and bought another 20 passion fruits. In the end, the number of passion fruits he had was ³₅ the number of pomegranates. How many more pomegranates than passion fruits did he have at first?

	Passion Fruits	Pomegranates	Total
Before	3 u - 20	4x5 = 20 u	670
Change	+ 20	- 3x5 = 15 u
After		1x5 = 5 u
Comparing between passion fruits and pomegranates	3x1 = 3 u	5x1 = 5 u

The number of pomegranates in the end is repeated. Make the number of pomegranates in the end the same. LCM of 1 and 5 is 5.

Total number of passion fruits and pomegranates at first
= 3 u - 20 + 20 u
= 23 u - 20

23 u - 20 = 670
23 u = 670 + 20
23 u = 690

1 u = 690 ÷ 23 = 30

Number of more pomegranates than passion fruits at first
= 20 u - (3 u - 20)
= 20 u - 3 u + 20
= 17 u + 20
= 17 x 30 + 20
= 510 + 20
= 530

Answer(s): 530