Question

Alex dumped out his piggy bank and there were only nickels, dimes, and quarters. There were eight less dimes than nickels, and four times as many quarters as nickels. If the total amount of money was $16.45, how many of each type of coin were there?

Answer 1

Alex has 15 nickels, 7 dimes, and 60 quarters. These numbers were found by setting up an equation with the relationships provided between the number of coins and solving for one variable.

Step-by-step explanation:

The student is working on a problem involving counting coins and total value calculation. Let n represent the number of nickels, d the number of dimes, and q the number of quarters in the piggy bank. According to the problem, the relationships between the numbers of coins are:

• d = n - 8
• q = 4n

The total value for the nickels, dimes, and quarters can be expressed as 5n + 10d + 25q = 1645 (since the total amount is $16.45 and we use pennies as the unit for simplicity).

Inserting the relationships into the value equation, we get:

• 5n + 10(n - 8) + 25(4n) = 1645

Simplifying gives:

• 5n + 10n - 80 + 100n = 1645
• 115n = 1645 + 80
• 115n = 1725
• n = 1725 / 115
• n = 15

Now that we know there are 15 nickels, we can find the number of dimes and quarters:

• d = n - 8 = 15 - 8 = 7 dimes
• q = 4n = 4 × 15 = 60 quarters

So, Alex has 15 nickels, 7 dimes, and 60 quarters in his piggy bank.