Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54. How many of each type of coin does Ari have?
$\square$ pennies and $\square$ nickels
Answer (1)
Let p be the number of pennies, so the number of nickels is 22 − p .
Set up the equation for the total value: 0.01 p + 0.05 ( 22 − p ) = 0.54 .
Solve for p : p = 14 .
Calculate the number of nickels: 22 − 14 = 8 . The final answer is 14 pennies and 8 nickels.
Explanation
Problem Analysis Let's analyze the problem. We know Ari has 22 coins in total, made up of pennies and nickels. We also know the total value of these coins is $0.54 . Our goal is to find out how many of each type of coin Ari has.
Setting up the Equation Let p be the number of pennies Ari has. Since the total number of coins is 22, the number of nickels will be 22 − p . The value of p pennies is 0.01 p dollars, and the value of ( 22 − p ) nickels is 0.05 ( 22 − p ) dollars. The total value of the coins is $0.54 , so we can set up the following equation: 0.01 p + 0.05 ( 22 − p ) = 0.54
Solving for Pennies Now, let's solve the equation for p :
0.01 p + 0.05 ( 22 − p ) = 0.54 0.01 p + 1.10 − 0.05 p = 0.54 − 0.04 p = 0.54 − 1.10 − 0.04 p = − 0.56 p = − 0.04 − 0.56 p = 14
Finding the Number of Nickels So, Ari has 14 pennies. Now we can find the number of nickels: Number of nickels = 22 − p = 22 − 14 = 8 .
Final Answer Therefore, Ari has 14 pennies and 8 nickels.
Examples
Imagine you're running a lemonade stand and need to keep track of your earnings. Knowing how to solve this type of problem can help you manage your cash. For example, if you have a mix of dimes and quarters totaling $5.00 , you can use a similar equation to figure out exactly how many of each coin you have, making sure your accounting is accurate and your cash handling is efficient.
