SOLUTION: Mike's average on five tests are 84,80,76,96,and 80. What must mike score on his sixth test so that his average will be 85?

Question 251071: Mike's average on five tests are 84,80,76,96,and 80. What must mike score on his sixth test so that his average will be 85?
Found 2 solutions by checkley77, PRMath:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
84,80,76,96,and 80
(84+80+76+96+80+X)/6=85
(416+X)/6=80 CROSS MULTIPLY.
416+X=480
X=480-416
X=64 IS THE REQUIRED TEST SCORE ON THE LAST TEST TO MAINTAIN AN AVERAGE OF 80.

Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
Mike's five tests are: 84, 80, 76, 96, and 80.
To find the average of grades, you would add those five grades and divide by 5, right?

BUT in this case, we want to know what he would need on a SIXTH test to have an average of 85. In other words, you are now going to add SIX scores together and then divide by SIX, so that you can try to reach the answer of 85.

So what is the sum of the five scores that Mike already has? Let's add them:

84 + 80 + 76 + 96 + 80 = 416

So, you need to add one more test to the total above, and then divide all of it (the 416 and the new test result) by 6, to get an 85.

The equation, then is this:

In other words, the sum of the five scores (416) plus an unknown sixth score (x) must all be divided by 6 to reach 85.

Now let's do the math:

416 + X = 510 (I multiplied by six on both sides of the equation to get rid of the denominator of 6. See how 85 times 6 = 510?)
X = 510 - 416 (I am subtracting 416 from both sides to isolate the "X")
X = 94

So, the last test must be a 94 for Mike to have an average of 85.

Let's check that:

84 + 80 + 76 + 96 + 80 + 94 = 510 ........AND

Yay.. it checks.

I hope this helps you. :-)
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