Final answer:
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:
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.