Question

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 currenty weighs 189 pounds and is losing 0.5 of a pound per week.Which models w, the number of weeks he should lose weight to be in the qualifying weight range?

Answer 1

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.

Step-by-step 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.