For a wrestler to qualify in his weight class, he needs to weigh more than 165 pounds but less than or equal to 185 pounds. He currently weighs 189 pounds and is losing 0.5 pounds per week.

Which models $ w $, the number of weeks he should lose weight to be in the qualifying weight range?

Question

20-08-2023
Biology

Middle School

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For a wrestler to qualify in his weight class, he needs to weigh more than 165 pounds but less than or equal to 185 pounds. He currently weighs 189 pounds and is losing 0.5 pounds per week.

Which models $ w $, the number of weeks he should lose weight to be in the qualifying weight range?

Answer :

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Donald1012 Donald1012 · Answer 1 · 2024-01-28T02:09:29-05:00

Final answer:

The wrestler should continue to lose weight for at least 8 weeks but no more than 48 weeks to be within the weight range for his class, assuming he loses 0.5 pounds per week.

Explanation:

To model the number of weeks w the wrestler should lose weight to fall within the qualifying weight range, one can set up an inequality. Currently, the wrestler weighs 189 pounds and needs to weigh more than 165 pounds but less than or equal to 185 pounds. Since he is losing 0.5 pounds per week, the equation representing his weight after w weeks can be written as:

189 - 0.5w > 165

189 - 0.5w ≤ 185

Solving the first inequality for w gives us:

189 - 165 > 0.5w

24 > 0.5w

48 weeks > w

This means it will take the wrestler less than 48 weeks to weigh more than 165 pounds. Now solving the second inequality:

189 - 185 ≤ 0.5w

4 ≤ 0.5w

8 weeks ≤ w

This indicates that it will take the wrestler at least 8 weeks to weigh 185 pounds or less.

To meet the requirements, the wrestler should continue to lose weight for at least 8 weeks but no more than 48 weeks.

For a wrestler to qualify in his weight class, he needs to weigh more than 165 pounds but less than or equal to 185 pounds. He currently weighs 189 pounds and is losing 0.5 pounds per week.Which models \( w \), the number of weeks he should lose weight to be in the qualifying weight range?

Answer :

Final answer:

Explanation:

Other Questions

For a wrestler to qualify in his weight class, he needs to weigh more than 165 pounds but less than or equal to 185 pounds. He currently weighs 189 pounds and is losing 0.5 pounds per week.

Which models \( w \), the number of weeks he should lose weight to be in the qualifying weight range?