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In Olympic diving, there are seven judges who rate the performance of each dive on a scale from 0 to 10, using half-point increments, where 0 is a failed attempt and 10 is excellent. After each of the seven judges has scored the dive, the two highest scores and the two lowest scores are discarded. The remaining three scores are then added together and the sum is multiplied by the degree of difficulty of the dive. This degree of difficulty is a number between 1.2 and 3.6. A famous Olympian diver completed a dive with degree of difficulty 3.5 and received the following seven performance scores from the judges: 8.0, 7.0, 8.5, 7.0, 7.5, 7.0, 7.0. What was the final number of points that the Olympian received on this dive? Express your answer as a decimal to the nearest tenth. 

 Jul 29, 2022
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Here's Mathcounts' solution: 

 

"The two highest scores are 8.5 and one of the two 8.0 scores, so these are discarded; the two lowest scores are 7.0 and 7.0 (both of the two 7.0 scores), so these are discarded. The scores that are used are the one remaining 8.0 and the two scores of 7.5. Therefore, the point total for the dive is 3.5(8.0 + 7.5 + 7.5) = 3.5(23) = 3(23) + 1 2 (23) = 69 + 11.5 = 80.5 points."

 Jul 29, 2022

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