Dropped Quiz and Final Exam Weight
A student has five quiz scores: 72, 85, 90, 68, and 88. The teacher drops the lowest quiz score and averages the remaining four. The final exam will count as two quiz scores. The student needs an overall average of at least 80 to earn a B. Final-exam scores are reported as whole numbers only, and the school rounds the final average to the nearest whole number for report cards. The student wants to know the lowest final-exam score that will earn a B, and also whether a score of 88 would earn an A- (average at least 90).
1. Calculate the lowest whole-number final-exam score that earns a B. Show the dropped score, the sum, and the inequality.
Read the worked answer
Drop the lowest score, 68. Remaining sum: 72 + 85 + 90 + 88 = 335. Let x be the final-exam score. The final counts twice, so the average is (335 + 2x) / 6.
Set the average to at least 80: (335 + 2x) / 6 ≥ 80 335 + 2x ≥ 480 2x ≥ 145 x ≥ 72.5
A whole-number score of 73 gives (335 + 146) / 6 = 481 / 6 = 80.17, which rounds to 80. But because the school rounds the average to the nearest whole number, a 72 also gives (335 + 144) / 6 = 479 / 6 = 79.83, which rounds to 80. So under the stated rounding policy the lowest whole-number score is 72; if the B threshold is applied before rounding, it is 73. The student should confirm which rule the teacher uses.
2. Would a final-exam score of 88 earn an A-? Show the average and apply the rounding rule.
Read the worked answer
With x = 88: (335 + 176) / 6 = 511 / 6 = 85.17, which rounds to 85-not 90. So 88 does not earn an A-.
In fact, an A- may be impossible. Even a perfect 100 gives (335 + 200) / 6 = 535 / 6 = 89.17, which rounds to 89. To reach an exact 90 average, the equation (335 + 2x) / 6 ≥ 90 requires 2x ≥ 205, so x ≥ 102.5-above the maximum score. The student cannot reach a 90 average under this weighting, regardless of the final exam.
3. The teacher considers counting the final as three quiz scores instead of two. Would that change the B threshold? Explain.
Read the worked answer
Yes, it changes the threshold. If the final counts three times, the average is (335 + 3x) / 7. Setting it to 80: 335 + 3x ≥ 560 3x ≥ 225 x ≥ 75.
With rounding, a 74 gives (335 + 222) / 7 = 557 / 7 = 79.57, which rounds to 80, so the lowest whole-number score would be 74 under the rounding policy. The heavier final weight raises the score needed compared with the two-score rule.