a cash register contains 165 coins consisting of pennies, nickles, and dimes. If the total number of nickels and dimes is equal to twice the number of pennies, and the total value of the coins is $7.95, find the number of each type of coin.

The number of

Pennies = 55 coins

Dimes = 38 coins

Nickels = 72 coins

Step-by-step explanation:

A penny is worth 1 cent. = 0.01p

A nickel is worth 5 cents = 0.05n

A dime is worth 10 cents = 0.10d

A cash register contains 165 coins consisting of pennies, nickels and dimes.

p + n + d = 165 coins

If the total number of nickels and dimes is equal to twice the number of pennies

n + d = 2p

We substitute

2p for n + d

p + n + d = 165 coins

p + 2p = 165

3p = 165

p = 165/3

p = 55 coins

n + d = 2p

n + d = 2(55)

n + d = 110

n = 110 - d

The total value of the coins is $7.95

0.01p + 0.05n + 0.10d = $7.95

We substitute

p = 55

n = 110 - d

0.01(55) + 0.05(110 - d) + 0.10d = 7.95

0.55 + 5.5 - 0.05d + 0.10d = 7.95

6.05 + 0.05d = 7.95

Collect like terms

0.05d = 7.95 - 6.05

0.05d = 1.9

d= 1.9/0.05

d = 38 coins

n = 110 - d

n = 110 - 38

n = 72 coins

The number of

Pennies = 55 coins

Dimes = 38 coins

Nickels = 72 coins