SOLUTION: A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth tes

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Question 334213: A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Think about how we take an average. We add up all of the numbers and divide by the number of numbers. The final average for our student will be the sum of all 4 test scores divided by 4. Let's say we want to achieve an overall average of for data elements given data elements.

We know that

So we can say that

But , the answer to the question, can be found by:

Which is to say:

So add up the scores for the tests already taken and subtract that sum from the product of the total number of tests multiplied by the desired overall average. Done.

John

My calculator said it, I believe it, that settles it