Questions: Perry has 24 coins that equal 52 cents. All the coins are pennies, (p), and nickels, (n). How many nickels and pennies does Perry have? Use the table to guess and check.
Types of Coins
(p) (n) (0+pi=24) (0+5 n=52)
5 nickels and 19 pennies
6 nickels and 18 pennies
7 nickels and 17 pennies
8 nickels and 16 pennies
Transcript text: Perry has 24 coins that equal 52 cents. All the coins are pennies, $p$, and nickels, $n$. How many nickels and pennies does Perry have? Use the table to guess and check.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{4}{|c|}{ Types of Coins } \\
\hline$p$ & $n$ & $0+\pi=24$ & $0+5 n=52$ \\
\hline & & & \\
\hline & & & \\
\hline & & & \\
\hline
\end{tabular}
5 nickels and 19 pennies
6 nickels and 18 pennies
7 nickels and 17 pennies
8 nickels and 16 pennies
Solution
Solution Steps
Step 1: Define the variables and equations
Let \( p \) represent the number of pennies and \( n \) represent the number of nickels. We are given two pieces of information:
The total number of coins is 24:
\[
p + n = 24
\]
The total value of the coins is 52 cents:
\[
1p + 5n = 52
\]
Step 2: Solve the system of equations
We can solve the system of equations using substitution or elimination. Here, we will use substitution.
From the first equation:
\[
p = 24 - n
\]
Substitute \( p = 24 - n \) into the second equation:
\[
1(24 - n) + 5n = 52
\]
\[
24 - n + 5n = 52
\]
\[
24 + 4n = 52
\]
\[
4n = 28
\]
\[
n = 7
\]
Now, substitute \( n = 7 \) back into the equation \( p = 24 - n \):
\[
p = 24 - 7 = 17
\]
Step 3: Verify the solution
Check that the values satisfy both original equations:
\( p + n = 17 + 7 = 24 \) (correct)
\( 1p + 5n = 17 + 35 = 52 \) (correct)
Final Answer
Perry has \\(\boxed{7 \text{ nickels and } 17 \text{ pennies}}\\).