Mayerlin needs to order some new supplies for the restaurant where she works. The restaurant needs at least 623 forks. There are currently 223 forks. If each set on sale contains 8 forks, write and solve an inequality which can be used to determine xx, the number of sets of forks Mayerlin could buy for the restaurant to have enough forks.

To solve this problem, we need to set up an inequality to represent the situation.

### Step 1: Define the variable
Let \( x \) represent the number of sets of forks Mayerlin needs to buy.

### Step 2: Determine the total number of forks needed
The restaurant needs at least 623 forks, and they already have 223 forks. So, the additional number of forks Mayerlin needs to buy is \( 623 - 223 = 400 \) forks.

### Step 3: Set up the inequality
Each set contains 8 forks, so the number of forks Mayerlin buys is \( 8x \), where \( x \) is the number of sets.

For the restaurant to have enough forks, the number of forks Mayerlin buys must be at least 400:
\[
8x \geq 400
\]

### Step 4: Solve the inequality
Now, solve for \( x \):
\[
x \geq \frac{400}{8}
\]
\[
x \geq 50
\]

### Conclusion
Mayerlin needs to buy **at least 50 sets** of forks for the restaurant to have enough.

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Would you like more details, or do you have any questions? 

Here are 5 related questions you might find helpful:
1. How would the inequality change if each set contained 10 forks instead of 8?
2. What if the restaurant already had 300 forks? How many sets would Mayerlin need to buy?
3. How would you set up an inequality if the restaurant needed exactly 623 forks?
4. What if the restaurant wanted to have more than 700 forks in total?
5. How would this problem change if Mayerlin could only buy whole sets of forks?

**Tip:** When solving inequalities, always pay attention to the direction of the inequality, especially when dividing or multiplying both sides by a negative number!

Learn how to solve the inequality to determine how many sets of forks Mayerlin needs to buy. The restaurant needs at least 623 forks, and each set contains 8 forks. A step-by-step solution shows how to use algebraic concepts to find the number of sets required. Suitable for students in Grades 6-8.

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