Josue has $$ \$ 0.33 $$ worth of pennies and nickels, He has a total of 13 pennics and nickels altogether. Write a system of equations that could be used to determine the number of pennics and the number of nickels that Josue has. Define the variables that you use to write the system.

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To determine the number of pennies and nickels Josue has, we can set up a system of equations based on the information provided.

### Define the Variables:
- **Let $$ p $$ represent the number of pennies.**
- **Let $$ n $$ represent the number of nickels.**

### Set Up the Equations:

1. **Total Number of Coins:**
   
   Josue has a total of 13 pennies and nickels combined.
   
   $$
   p + n = 13
   $$
   
2. **Total Value of the Coins:**
   
   - Each penny is worth \$0.01.
   - Each nickel is worth \$0.05.
   
   The combined value of the pennies and nickels is \$0.33.
   
   $$
   0.01p + 0.05n = 0.33
   $$

### Summary of the System of Equations:
$$
\begin{cases}
p + n = 13 \
0.01p + 0.05n = 0.33
\end{cases}
$$

### How to Use the System:
You can solve this system of equations using various methods such as substitution or elimination to find the values of $$ p $$ (number of pennies) and $$ n $$ (number of nickels).

**Example Using Substitution:**

1. **From the first equation:**
   $$
   p = 13 - n
   $$
   
2. **Substitute $$ p $$ in the second equation:**
   $$
   0.01(13 - n) + 0.05n = 0.33
   $$
   
3. **Solve for $$ n $$:**
   $$
   0.13 - 0.01n + 0.05n = 0.33 \
   0.13 + 0.04n = 0.33 \
   0.04n = 0.20 \
   n = 5
   $$
   
4. **Find $$ p $$:**
   $$
   p = 13 - 5 = 8
   $$
   
**Solution:**
Josue has **8 pennies** and **5 nickels**.
Let $$ p $$ be the number of pennies and $$ n $$ be the number of nickels. The system of equations is: $$ \begin{cases} p + n = 13 \ 0.01p + 0.05n = 0.33 \end{cases} $$

Josue has \( \$ 0.33 \) worth of pennies and nickels, He has a total of 13 pennics and nickels altogether. Write a system of equations that could be used to determine the number of pennics and the number of nickels that Josue has. Define the variables that you use to write the system.

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