# Simple algebra problem: Check my work please?

1. Jan 20, 2008

### Holocene

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

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

3. 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.

2. Jan 20, 2008

### rocomath

That's right.

3. Jan 20, 2008

### Holocene

Thanks.

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

4. Jan 20, 2008

### rocomath

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

5. Jan 20, 2008

### 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?

6. Jan 20, 2008

### HallsofIvy

Staff Emeritus
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.