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The problem describes a scenario where Farmer Yoy wants to sell tarts and plaques at a market, with certain price points and expected goals. Let me break down the problem and construct a system of inequalities based on the details:

1. **Tart price**: $4 per tart
2. **Plaque price**: $9 per plaque
3. **Expected income**: No less than $792
4. **Expected number of plaques**: At least 3 plaques

We need to write a system of inequalities to model the relationship between the number of tarts ($x$) and plaques ($y$) that can achieve these conditions.

### 1. Income inequality:
The total income from selling $x$ tarts and $y$ plaques is represented by:
\[
4x + 9y
\]
The income must be no less than $792, so we set up the inequality:
\[
4x + 9y \geq 792
\]

### 2. Plaque constraint:
The number of plaques should be at least 3, so we have the inequality:
\[
y \geq 3
\]

### System of inequalities:
\[
\begin{cases}
4x + 9y \geq 792 \\
y \geq 3
\end{cases}
\]

This system models the relationship between the number of tarts ($x$) and plaques ($y$) based on the problem conditions.

Would you like more details on solving this system or have any questions?

### Related questions:
1. How can you graph this system of inequalities?
2. What happens if Farmer Yoy wants to sell more than 3 plaques? How does it affect the solution?
3. Can you find specific values for $x$ and $y$ that satisfy the system?
4. How would the system change if the tart price increases to $5 per tart?
5. What if Farmer Yoy wants to make at least $1000 instead of $792?

**Tip:** When solving systems of inequalities, it's helpful to graph them to visualize the solution region where both inequalities are satisfied.

Farmer Yoy wanted to sell some tarts and plaques at the market. She planned to charge $4 per tart and $9 per plaque. She expected to make no less than $792. She expected to sell at least 3 plaques. Write a system of statements, in standard form, modeling the relationship between the amounts of tarts (x) and plaques (y).

Learn how to set up and solve a system of inequalities based on the scenario of Farmer Yoy selling tarts and plaques. This problem includes key algebraic concepts like income inequalities and constraints, suitable for students in Grades 7-9.

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