Once you know the lowest and highest possible cost for one package, think about what the lowest and highest possible totals would be for 9 packages. What operation connects a per-item cost to the total cost?

You should now have a minimum and maximum possible total shipping fee for 9 packages. Check which answer choices lie between these two numbers (including the endpoints).

For each answer choice, imagine dividing that total by 9. Would the resulting cost per package still be between $5$ and $7$ dollars?

In Desmos, type 9*5 on one line and 9*7 on another line. These two values are the smallest and largest possible total shipping fees for 9 packages.

Look at the two values you got from Desmos; the valid total must be between these two numbers, including them. Check each answer choice (41, 48, 68, 72) and see which one lies inside this interval.

The retailer charges at least $5$ and at most $7$ dollars for each package. Let the shipping fee for one package be $c$. Then this description means:

• $c$ is at least $5$: $c \ge 5$
• $c$ is at most $7$: $c \le 7$

So the cost per package satisfies $5 \le c \le 7$ (in words: $c$ is between $5$ and $7$, inclusive).

If 9 packages are shipped and each one costs between $5$ and $7$ dollars, then the smallest possible total cost happens when each package costs $5$, and the largest possible total happens when each package costs $7$.

• Minimum total: $9(5) = 45$
• Maximum total: $9(7) = 63$

So the total shipping fee for 9 packages must be between $45$ and $63$, including $45$ and $63$.

Now look at the answer choices: $41$, $48$, $68$, and $72$.

From Step 2, any possible total must be between $45$ and $63$.

• $41$ is less than $45$.
• $68$ and $72$ are greater than $63$.
• $48$ is between $45$ and $63$.

Therefore, the only total that could be the shipping fee for 9 packages is