Question

You are taking a course that has four tests. The first three tests are 100 points each and the fourth test is 200 points. To get an A in the course you must have an average of at least 90% on the four tests. Your scores on the first three tests were 87, 92, and 84. What must you score on the fourth test to get and A for the course?

Answer 1

The way I would think about this problem is like this...

The first 3 tests had 100 points available, and the last has 200 points available. so the course has 500 possible points.

To get an A, you need to average 90% overall, and 90% of 500 points is 450 points.

Since each of the first 3 tests had 100 points, your scores 87%, 92%, and 84% just happen to also be the number of points you received... so you scored 87, 92, and 84 points, respectively.

You can add those up to get your score through the first 3 tests: 87+92+84 = 263

And you need 450 total, so you need 450-263 = 187 points on the last test.

But remember, test 4 has 200 points available, so 187/200 is a percentage score of 93.5%

Answer 2

Hint:

Solve the following:
\[\frac{87 + 92 + 84 + x}{4} = 90\]