ISEE Word Problems Question 229: Answer and Explanation

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Question: 229

9. Buffy has taken 4 tests so far in her U.S. History class. Her scores on these tests are 72, 78, 81, and 85. The score on her final exam will be counted twice in her mean. What is the lowest score she can get on her final exam and have a mean score of no less than 80?

  • A. 84
  • B. 83
  • C. 82
  • D. 81

Correct Answer: C

Explanation:

The answer is C

Mean is determined by adding the scores and dividing by the number of scores, in this case 6 (because one test is counted twice). Let x represent the unknown score: = 80. Combine like terms in the numerator: = 80. Multiply both sides by 6, subtract 316 from both sides, and divide both sides by 2: x = 82.

A good way to think of mean is Total = Average × Number (TAN). Here, the number of tests is 6, and the desired average is 80. Thus, the total score when all 6 tests are added is 480 (80 × 6). As we have four of her scores, we can subtract them from the total: 480 - 72 - 78 - 81 - 85 = 164. Thus, 164 represents the remaining total score she needs to achieve her goal. As 164 represents the doubling of a single test score, divide it by 2. She must score 82 on h

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