Problem Solving- Weighted Average

[AndreaV424]

An instructor gives 3 initial exams and a final exam for a certain course. The average of the 3 initial exams was weighted 3.5 and the final exams is weighted 2/5. A student received initial exam grades of 72,73, and 80, and a final grade of x. If the students weighted average for the course was 79, what is the value of x?

a. 90
b. 87
c. 85
d. 84
e. 81

[truplayer256]

Average of 72,73, and 80= 145+80/(3)= 225/3= 75.

75*3/5+2/5(x)= 79

45+2/5(x)=79

34*5/2=x

x=17*5= 85

C

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Thanks trueplayer,

But if you could please explain why you multiplied 75 by 3/5?

Regards,
Niharika.

[shibal]

Because the avg of the 3 tests represent 3 5ths of the final grade... The last one is 2 5th

[sy323]

so the question should have said 3/5 instead of 3.5?

[GMATGuruNY]

An instructor gives 3 initial exams and a final exam for a certain course. The average of the 3 initial exams was weighted 3/5 and the final exams is weighted 2/5. A student received initial exam grades of 72,73, and 80, and a final grade of x. If the students weighted average for the course was 79, what is the value of x?

a. 90
b. 87
c. 85
d. 84
e. 81

The fraction in red above reflects the intent of the problem.

Since the final grade of x must account for 2/5 of the course -- in other words, for 2 of every 5 grades -- let the 5 grades be 72, 73, 80, x, x.

Since the average of the 5 grades is 79, we get:
Sum of the 5 grades = (number)(average) = 5*79 = 395.
Thus:
72+73+80+x+x = 395
2x = 170
x = 85.

The correct answer is C.