1 nickel = 5 cents = $0.05

1 dime = 10 cents = $0.10

1 quarter = 25 cents = $0.25

let

n = the number of nickels

d = the number of dimes

q = the number of quarters

There are 75 coins in the machine and the value of the coins is $7.25 = 725 cents

n + d + q = 75

5n + 10d + 25q = 725 divide both sides by 5

n + 2d + 5q = 145

here are 5 times as many nickels as dimes

n = 5d

by solving the system of equations

n + d + q = 75

n + 2d + 5q = 145

n = 5d

we find

n = 50 nickels

d = 10 dimes

q = 15 quarters

click here to see the step by step solution of the system of equations

Click to see all the steps

there are 50 nickles, 10 dimes and 15 quarters in the machine.

1 nickel = 5 cents = $0.05

1 dime = 10 cents = $0.10

1 quarter = 25 cents = $0.25

let

n = the number of nickels

d = the number of dimes

q = the number of quarters

There are 75 coins in the machine and the value of the coins is $7.25 = 725 cents

n + d + q = 75

5n + 10d + 25q = 725 divide both sides by 5

n + 2d + 5q = 145

here are 5 times as many nickels as dimes

n = 5d

by solving the system of equations

n + d + q = 75

n + 2d + 5q = 145

n = 5d

we find

n = 50 nickels

d = 10 dimes

q = 15 quarters

click here to see the step by step solution of the system of equations

Click to see all the steps

there are 50 nickles, 10 dimes and 15 quarters in the machine.