Question

Carmela opened her piggy bank and found she had $15.30. If she had only nickels, dimes, quarters, and half-dollars and an equal number of coins of each kind, how many coins did she have in all

Answer 1

68 coins

Explanation:

We can use the given information to write two equations involving the numbers of coins. One will express the total number of coins; the other will express their value.

__

setup

Since there are equal numbers of coins of each type, we can let n represent the number of each kind of coin. The total number coins will be ...

n +n +n +n + N . . . the sum of numbers of nickels, dimes, quarters, halves

The value of the coins is ...

0.05n +0.10n +0.25n +0.50n = 15.30

solution

The second equation lets us find the value of n:

0.90n = 15.30

n = 17 . . . . . . . . divide by 0.90

Then the number of coins in all is ...

4n = N

4(17) = N = 68

Carmela had 68 coins in all.