A student scores 87, 73, 92 and 86 on four exams during the semester, and 95 on the final exam. If the final is weighted double and the four others weighted equally, the student's final average would be 88.

Question

Quizplus · Accepted Answer

Let x be the weight of each of the four exams.

The average of the four exams is:

(87 + 73 + 92 + 86)/4 = 87

The weighted score of the four exams is:

x(87) + x(73) + x(92) + x(86) = 348x

The weighted score of the final exam is:

2(95) = 190

The total weighted score is:

348x + 190

The final average is:

(348x + 190)/5 = 88

Simplifying this equation gives:

348x + 190 = 440

348x = 250

x ≈ 0.72

Therefore, each of the four exams is weighted 0.72, and the final exam is weighted 1.44.

The weighted score of the four exams is:

0.72(87) + 0.72(73) + 0.72(92) + 0.72(86) = 250.56

The weighted score of the final exam is:

1.44(95) = 136.8

The total weighted score is:

250.56 + 136.8 = 387.36

And the final average is:

387.36/5 = 77.472

Therefore, the statement is false.

A Student Scores 87, 73, 92 and 86 on Four