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

the distance between point a and point b is 6 units

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: