How would you figure this question out

Question

My four test average is 85. I need a ? On my 5th test to average 88. 

Answer 1

Let's say you score a, b, c, and d on those first four tests. When you take the average of those, the question tells you, you get 85.

 

So (a + b + c + d)/4 = 85

 

Then a + b + c + d = 4(85) = 340.

 

If you were going to do the average of all five tests, including that last test you're trying to find the score of, it would look something like 

 

(a + b + c + d + ?)/5

 

Just up above, we were able to see that we can replace a + b + c + d with 340.

 

So the average of those five tests can be rewritten as

 

(340 + ?)/5

 

We want to find ? so that we get this to average to 88.

 

That means that 

 

(340 + ?)/5 = 88

 

So 340 + ? = 5(88) = 440

 

What do I add to 340 to get 440? Bummer. It has to be 100. That's impossible. I feel bad for that person.

Answer 2

For the sake of argument, let's say you're incredibly good at hitting the same score repeatedly on your tests. The first four tests, you got an 85 on each test to get an average of 85

 

Mean = (85 + 85 + 85 + 85) / 4

 

The mean here would be 85, obviously. There's four 85s, and you divide by 4. We now factor in a new test taken (one more to the denominator, add a variable to the top) and set our mean to equal 88

 

88 = (85 + 85 + 85 + 85 + x) / 5

 

We now do some algebra

 

88 * 5 = (85 + 85 + 85 + 85 + x)

 

88 * 5 - 85 * 4 = x

 

440 - 340 = x

 

x = 100

 

Brutal, you can't score higher than an 88 in the class with the next test.

Answer 3

The average is the sum of the scores divided by the number of scores.

If the average of 4 tests is 85, then the sum of the 4 tests is 85x4 = 340

 

If you need to get an 88 average of 5 scores, then

(340+x)/5 = 88, where x is the score on the 5th test.

 

340+x

-------  = 88

   5

 

340 + x = 440    Multiply both sides by 5

x = 100              Subtract 340 from both sides.