Which term should go with $b$ (bottles at $9$ each), and which should go with $p$ (backpacks at $24$ each)? Look carefully at the numbers in front of $b$ and $p$ in each option.

Does "at most" mean the total cost must be less than, greater than, or equal to $300$? Which inequality symbol matches that idea?

Should the costs of bottles and backpacks be added together or is there any reason to subtract one from the other?

In Desmos, type 9b + 24p to represent the total cost of buying $b$ bottles and $p$ backpacks. (Desmos will treat $b$ and $p$ as variables.)

Type each answer choice’s inequality into Desmos (for example, 9b + 24p <= 300) as separate lines. This will graph different shaded regions representing all $(b,p)$ pairs that satisfy each inequality.

Think about the meaning: the region that makes sense should include points where both $b$ and $p$ are nonnegative and where the sum of the costs doesn’t go over $300$. Look for the graph where the boundary line corresponds to spending exactly $300$ and the shaded region represents spending $300$ or less.

Each water bottle costs $9$ dollars and there are $b$ bottles, so the total cost of bottles is $9b$.

Each backpack costs $24$ dollars and there are $p$ backpacks, so the total cost of backpacks is $24p$.

So, the total cost of all items together is the sum of these:

The club has a budget of at most $300$ dollars.

• "At most $300$" means the total cost cannot be more than $300$.
• In math, "cannot be more than $300$" is written using the less than or equal to symbol: $\le 300$.

So the inequality must compare the total cost $9b + 24p$ to $300$ using $\le$.

Now combine the total cost expression and the budget comparison:

• Total cost: $9b + 24p$
• Must be less than or equal to $300$ dollars.

This gives the inequality

So the inequality that represents all affordable combinations of water bottles and backpacks is $9b + 24p \le 300$. This matches answer choice A.