Arya had some gold and silver stars. 4/9 of his stars were gold. After buying another 273 silver stars, 68% of the stars he had in the end were silver. How many stars did Arya have at first?
Let Arya have at first x stars
Number of gold stars = 4/9x
Number of silver stars = x - 4/9x = 5/9x
He buys 273 silver stars, so number of silver stars will be = 5/9x + 273
Since this is equal to 68% of total stars, it follows that:
5/9x + 273 = 68% of (x + 273)
5/9x + 273 = (68(x + 273))/100
(5x + 2457)/9 = (68x + 18564)/100
500x + 245700 = 612x + 167076
78624 = 112x
=> x = 702
Hence, Arya had 702 stars at first