Question

Kevin needs to order some new supplies for the restaurant where he works. The restaurant needs at least 491 glasses. There are currently 333 glasses. If each set on sale contains 18 glasses, which inequality can be used to determine xx, the minimum number of sets of glasses Kevin should buy?

Answer 1

To determine the minimum number of sets of glasses Kevin should buy, we first need to figure out how many additional glasses are needed.

Kevin currently has 333 glasses and needs at least 491 glasses. Therefore, the number of additional glasses required is:

\[
491 - 333 = 158
\]

Each set contains 18 glasses. If \( x \) represents the number of sets of glasses Kevin needs to buy, then the total number of glasses he will get from buying \( x \) sets is \( 18x \).

To find the minimum number of sets \( x \) that Kevin should buy to meet or exceed the requirement, we set up the following inequality:

\[
333 + 18x \geq 491
\]

Subtracting 333 from both sides gives:

\[
18x \geq 491 - 333
\]

This simplifies to:

\[
18x \geq 158
\]

To solve for \( x \), we divide both sides by 18:

\[
x \geq \frac{158}{18}
\]

Calculating \( \frac{158}{18} \):

\[
\frac{158}{18} \approx 8.7777
\]

Since \( x \) must be a whole number (you can't buy a fraction of a set), we round up to the next whole number. Thus, the minimum number of sets Kevin needs to buy is 9.

Putting this into an inequality form, to determine the minimum number of sets of glasses Kevin should buy, the relevant inequality is:

\[
x \geq \frac{158}{18}
\]

Or, equivalently:

\[
x \geq 9
\]

Therefore, the answer is:

\[
18x \geq 158
\]