change machine contains nickels, dimes, and quarters. There are 75 coins in the machine. The value of the coins is $7.25. There are 5 times as many nickels as dimes. How many quarters are in the machine?
Let x be the number of dimes.
The number of nickels is 5x.
The number of quarters is 75 - x - 5x = 75-6x.
The value of the dimes is 10x cents.
The value of the nickels is 5 * 5x = 25x cents.
The value of the quarters is 25 * (75 - x - 5x) = 1875 - 30x cents.
The total value of the coins is 10x + 25x + 1875 - 30x = 725 cents.
45x + 1875 - 30x = 725 cents.
15x + 1875 = 725 cents.
15x = 725 - 1875 cents.
15x = 1150 cents.
x = 1150 / 15 cents.
x = 76 nickels.
Hence, the number of quarters is 75 - 6 * 76 = 75 - 456 = 321 quarters. Answer: \boxed{321}.