Janelle has 342 pennies , 62 nickels,and 12 dimes. If Janelle exchanges her coins for dollars, how many dollars will she have? How much cent will remain
The Correct Answer and Explanation is:
To determine how much money Janelle will have in total, let’s calculate the total value of each type of coin in cents and then convert it to dollars.
- Calculate the value of pennies:
- Janelle has 342 pennies.
- Since each penny is worth 1 cent, the total value in cents is:
[
342 \times 1 = 342 \text{ cents}
]
- Calculate the value of nickels:
- Janelle has 62 nickels.
- Each nickel is worth 5 cents, so the total value in cents is:
[
62 \times 5 = 310 \text{ cents}
]
- Calculate the value of dimes:
- Janelle has 12 dimes.
- Each dime is worth 10 cents, so the total value in cents is:
[
12 \times 10 = 120 \text{ cents}
]
- Add up the total value in cents:
- Now, we sum up the values of all the coins:
[
342 + 310 + 120 = 772 \text{ cents}
]
- Convert the total amount from cents to dollars:
- There are 100 cents in a dollar, so we divide the total number of cents by 100 to get the amount in dollars:
[
\frac{772}{100} = 7 \text{ dollars and } 72 \text{ cents}
]
So, Janelle will have 7 dollars and 72 cents after exchanging her coins.
Explanation
Breaking down the calculation by each type of coin helps us to accurately account for the total amount. By first calculating each coin type’s value, we minimize the chance of errors and ensure we convert cents to dollars correctly. Since 100 cents equal 1 dollar, dividing by 100 gives us the dollar amount. The result of 7 dollars and 72 cents represents the total value of all Janelle’s coins combined.
This approach—breaking down calculations, summing values, and converting units—ensures accuracy in dealing with mixed denominations. Understanding these steps is especially helpful in real-life situations where coin-counting can lead to practical financial skills, such as budgeting and money management.