Question

A piggy bank is full of nickels, dimes, and quarters worth $3.30. If there are three times as many nickels as quarters, and half as many dimes as nickels, how many of each kind are there?

a) Nickels: 30, Dimes: 10, Quarters: 5
b) Nickels: 15, Dimes: 5, Quarters: 3
c) Nickels: 20, Dimes: 10, Quarters: 4
d) Nickels: 25, Dimes: 5, Quarters: 2

Answer 1

There are 6 quarters, 18 nickels, and 9 dimes in the piggy bank when solving the problem using the mathematical relationships provided, which differ from all the options listed.

Step-by-step explanation:

The problem requires us to find out the number of nickels, dimes, and quarters in the piggy bank that amount to $3.30, with the given relationships between the quantities of the coins.

Step-by-Step Solution:

1. Let the number of quarters be q. Then, according to the problem, the number of nickels is 3q, and the number of dimes is half as many nickels, which is ½ × 3q = 1.5q.
2. Equate the total value of the coins to $3.30 in cents: (25q + 5 × 3q + 10 × 1.5q) = 330 cents.
3. Simplify the equation: 25q + 15q + 15q = 330.
4. Combine like terms: 55q = 330.
5. Divide both sides by 55 to find q: q = 6.
6. Substitute q back into the expressions for nickels and dimes: there are 3q = 18 nickels and 1.5q = 9 dimes.

There are 6 quarters, 18 nickels, and 9 dimes. This is not one of the options provided, which indicates there may have been an error in the options or in the stipulated total amount. However, based on the mathematical relationships provided in the question, the correct numbers of each type of coin are 6 quarters, 18 nickels, and 9 dimes.