The fuel A costs $4 per gallon, and fuel B costs $8 per gallon. Peter can spend at most $24 on fuel. Write the system of linear inequalities to represent this situation.
4x + 8y < 24, x < 0 and y < 0
4x + 8y < 24, x > 0 and y > 0
4x + 8y ≤ 24, x ≤ 0 and y ≤ 0
4x + 8y ≤ 24, x ≥ 0 and y ≥ 0

The correct system of inequalities that represents this situation is:

\[
4x + 8y \leq 24, \quad x \geq 0, \quad y \geq 0
\]

Explanation:

- $x$ represents the gallons of fuel A purchased, and $y$ represents the gallons of fuel B purchased.
- The total cost for fuel A is $4x$, and the total cost for fuel B is $8y$.
- Peter can spend at most $24 on fuel, which leads to the inequality $4x + 8y \leq 24$.
- Since Peter cannot purchase a negative amount of fuel, both $x$ and $y$ must be non-negative, so $x \geq 0$ and $y \geq 0$.

Would you like further details on how this inequality was set up, or any other questions?

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Here are 5 related questions:
1. How can we graph this system of inequalities?
2. What is the solution region for the inequality $4x + 8y \leq 24$?
3. What happens if the cost per gallon of fuel A or fuel B changes?
4. Can Peter purchase only fuel A or only fuel B? How would that affect the inequalities?
5. How do we interpret the boundary line of the inequality $4x + 8y = 24$?

**Tip:** When solving systems of inequalities, always pay attention to whether the inequality is strict ($<$) or includes equality ($\leq$) to determine if the boundary is included in the solution set.

The fuel A costs $4 per gallon, and fuel B costs $8 per gallon. Peter can spend at most $24 on fuel. Write the system of linear inequalities to represent this situation.

Solve the system of linear inequalities where fuel A costs $4 per gallon and fuel B costs $8 per gallon. Peter has a budget of $24. Learn how to set up and interpret the inequalities 4x + 8y ≤ 24, with x and y representing non-negative amounts of fuel purchased. Suitable for Grades 9-12.

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