https://file.aiquickdraw.com/mathbot/file/17266085696479fqk8qw1.jpg

The problem in the image is:

"Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.? Write and solve an inequality to represent the situation."

### Step-by-Step Solution:

Let \( w \) represent the number of weeks Ryan will need to lose weight.

- Current weight: 200 lbs.
- Target weight: less than 175 lbs.
- Weekly weight loss: 2 lbs.

We need to set up an inequality. After \( w \) weeks, Ryan's weight will be:

\[
\text{Weight after } w \text{ weeks} = 200 - 2w
\]

We want his weight to be less than 175 lbs:

\[
200 - 2w < 175
\]

### Solving the inequality:

\[
200 - 2w < 175
\]
Subtract 200 from both sides:

\[
-2w < 175 - 200
\]

\[
-2w < -25
\]

Now, divide both sides by -2. Since we're dividing by a negative number, we need to reverse the inequality sign:

\[
w > \frac{-25}{-2}
\]

\[
w > 12.5
\]

### Conclusion:

Ryan needs more than 12.5 weeks to reach a weight of less than 175 lbs. Therefore, it will take him **at least 13 weeks** to weigh less than 175 lbs.

---

Would you like further details on this? Here are five related questions to deepen your understanding:

1. What happens if Ryan increases his weekly weight loss to 3 lbs. per week? How would that change the solution?
2. How would the inequality change if Ryan's target weight was 180 lbs. instead of 175 lbs.?
3. Can you graph the inequality \( 200 - 2w < 175 \) on a number line?
4. What is the significance of reversing the inequality when dividing by a negative number?
5. How could we modify this problem if Ryan gains weight instead of losing it?

### Tip:
Always remember to reverse the inequality sign when dividing or multiplying by a negative number during the solution of inequalities!

Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.? Write and solve an inequality to represent the situation.

Learn how to solve a weight loss problem using inequalities. Ryan needs to lose 2 lbs. per week to get under 175 lbs. from his current weight of 200 lbs. This step-by-step solution demonstrates how to write and solve the inequality. Suitable for students in Grades 6-8.

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