Final exam score needed for 90 average with weighted final

[Holocene]

Homework Statement

The grade in a class is determined by three tests and a final exam. The final exam counts twice as much as a test. A student's three test grades are 78, 82, and 100. What does he need to score on the final exam to bring his average up to 90?

Homework Equations

Please check this work; book is not giving this answer as a solution.

The Attempt at a Solution

$$\displaystyle{\frac{78 + 82 + 100 + 2x}{4} = 90}$$

$$\displaystyle{\frac{260 + 2x}{4} = 90}$$

$$\displaystyle{260 + 2x = 360}$$

$$\displaystyle{2x = 100}$$

$$\displaystyle{x = 50}$$

The student needs a score of 50 on the final exam to yeild an overall average of 90.

 

[rocomath]

That's right.

 

[Holocene]

That's right.

Thanks.

Book is giving "95" as an answer...

 

[rocomath]

Thanks.

Book is giving "95" as an answer...

I'm going to laugh if that's right, but I don't think it is :-]

 

[zhentil]

What?! That's really, really wrong. You need to be dividing by 5, not 4.

It helps to do a quick reality check on these. His average right now is not a 90. How on Earth would failing a test bring his score up?

 

[HallsofIvy]

zhentil is correct. If you are going to count the final exam as worth 2x in the numerator then you must count it as 2 tests in the denominator.