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The problem states the following:

- Abigail works as a salesperson selling phones and phone accessories.
- She earns:
  - \$12 commission for each phone sold,
  - \$3 commission for each accessory sold.
  
On a given day:
- Abigail made \$258 in total commission.
- She sold 6 more accessories than phones.

### Defining Variables:
Let:
- $ p $ = the number of phones sold.
- $ a $ = the number of accessories sold.

### Writing the System of Equations:
From the problem, we can write two equations:
1. The total commission equation:
   \[
   12p + 3a = 258
   \]
2. The equation for the relationship between phones and accessories:
   \[
   a = p + 6
   \]

Thus, the system of equations is:
\[
\begin{aligned}
12p + 3a &= 258 \\
a &= p + 6
\end{aligned}
\]

These equations can now be solved simultaneously to find the number of phones and accessories sold.

Would you like me to solve the system? If so, I can proceed! 

---
Here are some related questions that can deepen your understanding:
1. What method can be used to solve the system of equations (e.g., substitution or elimination)?
2. How would the equations change if Abigail sold fewer accessories than phones?
3. What would happen if Abigail's commission rates for phones and accessories were swapped?
4. How does the total commission change if she sells twice as many accessories but the same number of phones?
5. What happens to the system if Abigail earned commission on a different item, such as tablets?

**Tip**: When solving systems of equations, substitution is often the simplest method when one equation is already solved for a variable, like $ a = p + 6 $.

Abigail works as a salesperson at an electronics store and sells phones and phone accessories. Abigail earns a $12 commission for every phone she sells and a $3 commission for every accessory she sells. On a given day, Abigail made a total of $258 in commission and sold 6 more accessories than phones. Write a system of equations that could be used to determine the number of phones sold and the number of accessories sold. Define the variables that you use to write the system.

Learn how to solve a system of linear equations based on a real-world problem where Abigail sells phones and accessories with given commissions. This problem helps students practice writing and solving systems of equations. Suitable for Grades 7-9.

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