Ethan had a total of 785 mangosteens and passion fruits. He sold ²₅ of the passion fruits and bought another 27 mangosteens. In the end, the number of mangosteens he had was ¹₅ the number of passion fruits. How many more passion fruits than mangosteens did he have at first?

	Mangosteens	Passion Fruits	Total
Before	3 u - 27	5x5 = 25 u	785
Change	+ 27	- 2x5 = 10 u
After		3x5 = 15 u
Comparing between mangosteens and passion fruits	1x3 = 3 u	5x3 = 15 u

The number of passion fruits in the end is repeated. Make the number of passion fruits in the end the same. LCM of 3 and 5 is 15.

Total number of mangosteens and passion fruits at first
= 3 u - 27 + 25 u
= 28 u - 27

28 u - 27 = 785
28 u = 785 + 27
28 u = 812

1 u = 812 ÷ 28 = 29

Number of more passion fruits than mangosteens at first
= 25 u - (3 u - 27)
= 25 u - 3 u + 27
= 22 u + 27
= 22 x 29 + 27
= 638 + 27
= 665

Answer(s): 665