SOLUTION: A person's average was 64%. One the next test he got 68%. This raised his average to 65%. The next test, his average improved by 1% again. What did he get on the last test? I thou

Algebra ->  Average -> SOLUTION: A person's average was 64%. One the next test he got 68%. This raised his average to 65%. The next test, his average improved by 1% again. What did he get on the last test? I thou      Log On


   



Question 808437: A person's average was 64%. One the next test he got 68%. This raised his average to 65%. The next test, his average improved by 1% again. What did he get on the last test?
I thought of doing trial and error: I tried adding everything and dividing by the amount plus the number of extra 64s, but it took too long. I still don't know what the answer is. Please help me!

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We assume the 64% average was the average of n tests.
THe sum of the grades of those n tests was
64n .
When the next test grade was 68%, the sum of the grades of all the tests was
64n%2B68 , and since there were n%2B1 tests by then,
the average was %2864n%2B68%29%2F%28n%2B1%29 .
We are told that average was 65%, so
%2864n%2B68%29%2F%28n%2B1%29=65 --> 64n%2B68=65%28n%2B1%29 --> 64n%2B68=65n%2B65 --> 68-65=65n-64n --> 3=n .
So the average was 64% after 3 tests and 65% after 4 tests.
After the 5th test, the average was 1% higher (than 65%),
so it was 65% + 1% = 66%.
The sum of the first 4 tests was 65%2A4=260
With a percentage score of x on the fifth test,
the sum of the grades on the first 5 tests is
260%2Bx
The average for the first 5 tests can be calculated as
%28260%2Bx%29%2F5
and since the average is 66%,
%28260%2Bx%29%2F5=66 --> 260%2Bx=66%2A5 --> 260%2Bx=330 --> x=330-260 --> highlight%28x=70%29