Madison needs to order some new supplies for the restaurant where she works. The restaurant needs at least 400 spoons. There are currently 219 spoons. If each set on sale contains 18 spoons, which inequality can be used to determine xx, the minimum number of sets of spoons Madison should buy?

Answer 1

To determine the minimum number of sets of spoons Madison should buy, we need to set up an inequality based on the total number of spoons required.

1. The restaurant needs at least 400 spoons.
2. Currently, there are 219 spoons.
3. Each set contains 18 spoons.

Let \( x \) be the number of sets of spoons Madison buys. The total number of spoons after purchasing \( x \) sets can be expressed as:

\[ \text{Total spoons} = 219 + 18x \]

We need this total to be at least 400 spoons, so we set up the inequality:

\[ 219 + 18x \geq 400 \]

Now, we can isolate \( x \) by solving this inequality:

1. Subtract 219 from both sides: \[ 18x \geq 400 - 219 \] \[ 18x \geq 181 \]

2. Divide both sides by 18: \[ x \geq \frac{181}{18} \]

Calculating \( \frac{181}{18} \) gives approximately 10.06, meaning Madison needs to buy at least 11 sets since she can't buy a fraction of a set.

Thus, the final inequality is:

\[ 219 + 18x \geq 400 \]

This inequality can be used to determine the minimum number of sets \( x \) that Madison should buy.