Burgess Hart
09/18/2023 · High School

26. DRAWING CONCLUSIONS The winner of a weight-lifting competition bench-pressed 400 pounds. The other competitors all bench-pressed at least 23 pounds less. a. Write an inequality that represents the weights that the other competitors bench-pressed. b. Was one of the other competitors able to bench-press 379 pounds? Explain.

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a. Let \( x \) represent the weight that the other competitors bench-pressed. Since the winner bench-pressed 400 pounds and the other competitors bench-pressed at least 23 pounds less, we can write the inequality as: \[ x \leq 400 - 23 \] Calculating the right side: \[ x \leq 377 \] So the inequality that represents the weights that the other competitors bench-pressed is: \[ x \leq 377 \] b. To determine if one of the other competitors was able to bench-press 379 pounds, we can compare 379 pounds to the maximum weight they could bench-press, which is 377 pounds (from the inequality we established). Since \( 379 > 377 \), it is not possible for any of the other competitors to bench-press 379 pounds. Therefore, the answer is no; one of the other competitors was not able to bench-press 379 pounds.

Quick Answer

a. The inequality for the other competitors' bench-pressed weights is \( x \leq 377 \). b. No, none of the other competitors could bench-press 379 pounds.
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