Exam grades are 76, 85, and 80. Course grade is 80. What is the weight of each exam grade?

Question

Exam grades are 75, 85, and 80. Oveall course grade is 80. What is the weight of each exam grade?

Answer 1

A grade (percent) multiplied by the weight gives the percent of the overall grade:

For example, 90 counting 50%, 95 counting 30%, and 100 counting 20% (note: total 100%)

gives a grade of 0.50*90 + 0.30*95 + 0.20*100 = 93.5

a + b + c = 1.00 [1.00 is 100%; percents add up to 100% or 1.00]

76a + 85b + 80c = 80 [course grade]

80a + 80b + 80c = 80 [We would get an aver=80 if we got all 80]'s]

------------------------------------------- [elimination; subtract equations]

-4a + 5b = 0

4a = 5b

b = (4/5)a

b = ..8a

As long as a is four-fifths of b, the course grade will be 80.

Weights

a b c

------- ------- -------

50% 40% 10% [note: 10% is needed to make total 100%]

25% 20% 55%

. . .

With whole percents, there are many possible answers.

5% 4% 91%

10% 8% 82%

15% 32% 73%

29% 16% 64%

25% 20% 55%

30% 24% 35%

35% 28% 37%

45% 36% 19%

50% 40% 10%

55% 44% 1%