If the same amount (between 1.2 and 1.5 cups) is used for each of 40 batches, what operation connects the per-batch amount to the total amount for 40 batches?

Write an inequality that shows the sugar per batch is between 1.2 and 1.5 cups, then multiply all parts of that inequality by 40 to represent 40 batches. Which option shows that relationship for $s$, the total sugar?

In Desmos, type 1.2*40 on one line and 1.5*40 on another line. Look at the two numerical outputs; these give the smallest and largest possible total cups of sugar for 40 batches.

Compare the two numbers you got in Desmos with each answer choice. Identify the option where $s$ is written as being at least the smaller number and at most the larger number, with each bound obtained by multiplying 1.2 and 1.5 by 40.

The problem says the bakery uses between 1.2 and 1.5 cups of sugar to make one batch.

We can write this as an inequality for the sugar per batch (call it $x$):

This means each single batch uses at least $1.2$ cups and at most $1.5$ cups of sugar.

If one batch uses $x$ cups of sugar, then 40 batches use a total of $s = 40x$ cups.

To find the range for the total $s$, multiply each part of the per-batch inequality by 40:

This gives the lower and upper bounds for the total sugar used in 40 batches.

We defined the total sugar as $s = 40x$, so the middle term $40x$ is just $s$.

Replace $40x$ with $s$ in the inequality from Step 2 to get:

This matches answer choice B, so $(1.2)(40) \le s \le (1.5)(40)$ is the correct inequality for the possible total cups of sugar used in the month.