Question

Serenity needs to order some new supplies for the restaurant where she works. The restaurant needs at least 574 glasses. There are currently 355 glasses. If each set on sale contains 12 glasses, which inequality can be used to determine xx, the minimum number of sets of glasses Serenity should buy?

Answer 1

To determine the minimum number of sets of glasses Serenity should buy, we start by figuring out how many more glasses are needed beyond the current 355 glasses. The total required glasses are at least 574.

1. Calculate the additional glasses needed:
\[
574 - 355 = 219
\]

2. Let \( x \) represent the number of sets of glasses Serenity should buy. Since each set contains 12 glasses, the total number of glasses from \( x \) sets will be \( 12x \).

3. Aiming for at least 574 glasses, the inequality can be established as follows:
\[
355 + 12x \geq 574
\]

4. To simplify the inequality:
\[
12x \geq 574 - 355
\]
\[
12x \geq 219
\]

5. Finally, dividing both sides by 12 gives:
\[
x \geq \frac{219}{12}
\]
\[
x \geq 18.25
\]

Since \( x \) must be a whole number (you can't order a fraction of a set), we round up to the nearest whole number. Thus, the minimum number of sets Serenity should buy is:
\[
x \geq 19
\]

The final inequality that can be used to determine the minimum number \( x \) of sets of glasses is:
\[
12x \geq 219
\]