Question

going into the final exam, which will count as two tests, brandi has test scores of 75, 84, 70, 59, and 90. what score does brandi need on the final in order to have an average score of 80? brandi needs a score of \square.

Explanation:

Step1: Define variables and average formula

Let \( x \) be the score on the final (counts as 2 tests). Total tests: \( 4 + 2 = 6 \). Average formula: \( \frac{\text{Total Score}}{\text{Total Tests}} = 80 \).

Step2: Calculate total current score

Current scores: 75, 84, 70, 59, 90. Sum: \( 75 + 84 + 70 + 59 + 90 = 378 \).

Step3: Set up equation for average

Total score with final: \( 378 + 2x \) (since final is 2 tests). Average: \( \frac{378 + 2x}{6} = 80 \).

Step4: Solve for \( x \)

Multiply both sides by 6: \( 378 + 2x = 480 \). Subtract 378: \( 2x = 102 \). Divide by 2: \( x = 51 \). Wait, that can't be right. Wait, no—wait, the final counts as two tests, so total number of test scores is 4 (existing) + 2 (final) = 6? Wait, no, existing scores: 75, 84, 70, 59, 90—wait, that's 5 scores? Wait, the problem says "Brandi has test scores of 75, 84, 70, 59, and 90"—so 5 tests, and the final counts as two tests. So total tests: 5 + 2 = 7? Wait, I misread. Let's correct:

Existing scores: 5 tests (75,84,70,59,90). Final: 2 tests. Total tests: 5 + 2 = 7. Average desired: 80. So total score needed: \( 80 \times 7 = 560 \).

Current total: \( 75 + 84 + 70 + 59 + 90 = 378 \). Let final score (for each of the two tests) be \( x \), so total from final: \( 2x \). So \( 378 + 2x = 560 \). Then \( 2x = 560 - 378 = 182 \). Then \( x = 91 \). Ah, I see—earlier mistake: number of existing tests. Let's redo:

Step1: Correct number of tests

Existing tests: 5 (75,84,70,59,90). Final: 2 tests. Total tests: 5 + 2 = 7.

Step2: Total score needed for average 80

Total score: \( 80 \times 7 = 560 \).

Step3: Current total score

\( 75 + 84 = 159 \); \( 159 + 70 = 229 \); \( 229 + 59 = 288 \); \( 288 + 90 = 378 \).

Step4: Score needed from final (2 tests)

Let final score (each test) be \( x \), so total from final: \( 2x \). So \( 378 + 2x = 560 \).

Step5: Solve for \( x \)

\( 2x = 560 - 378 = 182 \). \( x = 91 \). Wait, that makes sense. Wait, earlier I thought 4 existing tests, but it's 5. Let's check again: the problem says "test scores of 75, 84, 70, 59, and 90"—that's 5 scores. So 5 tests, final is 2 tests. Total 7 tests. So average 80: total 560. Current total: 75+84=159, +70=229, +59=288, +90=378. So 560-378=182. 182/2=91. So Brandi needs a score of 91 on each of the two final tests? Wait, the problem says "what score does Brandi need on the final"—assuming the final is a single test that counts as two, so the score on the final (the test) is \( x \), and it's weighted as two tests. So yes, the calculation is correct.

Answer:

91