Answer:
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
