Question
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.
Answers
GPT-4o mini
To determine how many sets of forks Mayerlin should buy, we can set up an inequality based on the number of forks she currently has and the number of forks needed.
Let \( x \) be the number of sets of forks to be bought. Each set contains 8 forks.
The total number of forks after buying \( x \) sets will be the current number of forks plus the number of forks in the new sets:
\[
223 + 8x
\]
We need this total to be at least 623 forks:
\[
223 + 8x \geq 623
\]
Now, we will solve the inequality:
1. Subtract 223 from both sides:
\[
8x \geq 623 - 223
\]
\[
8x \geq 400
\]
2. Divide both sides by 8:
\[
x \geq \frac{400}{8}
\]
\[
x \geq 50
\]
Thus, the inequality \( x \geq 50 \) indicates that Mayerlin must buy at least **50 sets** of forks to have enough for the restaurant.
Let \( x \) be the number of sets of forks to be bought. Each set contains 8 forks.
The total number of forks after buying \( x \) sets will be the current number of forks plus the number of forks in the new sets:
\[
223 + 8x
\]
We need this total to be at least 623 forks:
\[
223 + 8x \geq 623
\]
Now, we will solve the inequality:
1. Subtract 223 from both sides:
\[
8x \geq 623 - 223
\]
\[
8x \geq 400
\]
2. Divide both sides by 8:
\[
x \geq \frac{400}{8}
\]
\[
x \geq 50
\]
Thus, the inequality \( x \geq 50 \) indicates that Mayerlin must buy at least **50 sets** of forks to have enough for the restaurant.