Question

1. ryan is a wrestler trying to make weight. he currently weighs 200 lbs. if he loses 2 lbs. per week (w), how many weeks will it take him to weigh 175 lbs. or less? inequality: it will take ryan weeks to weigh 175 lbs. or less.

Explanation:

Step1: Define the inequality

Ryan starts at 200 lbs and loses 2 lbs per week (\(w\)). We want his weight to be 175 lbs or less. So the inequality is \(200 - 2w \leq 175\).

Step2: Solve for \(w\)

Subtract 200 from both sides: \(-2w \leq 175 - 200\)
Simplify: \(-2w \leq -25\)
Divide both sides by -2 (remember to reverse the inequality sign): \(w \geq \frac{-25}{-2}\)
Simplify: \(w \geq 12.5\)

Since we can't have half a week in this context (or if we consider whole weeks, we need to round up), but mathematically the solution is \(w \geq 12.5\). If we need whole weeks, it will take 13 weeks (but the inequality solution is \(w \geq 12.5\)).

Answer:

The inequality is \(200 - 2w \leq 175\) and it will take at least 12.5 weeks (or 13 whole weeks) for Ryan to weigh 175 lbs or less. If we consider the inequality solution for \(w\), \(w \geq 12.5\).