Question 808437
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+68}}} , and since there were {{{n+1}}} tests by then,
the average was {{{(64n+68)/(n+1)}}} .
We are told that average was 65%, so
{{{(64n+68)/(n+1)=65}}} --> {{{64n+68=65(n+1)}}} --> {{{64n+68=65n+65}}} --> {{{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*4=260}}}
With a percentage score of {{{x}}} on the fifth test,
the sum of the grades on the first 5 tests is
{{{260+x}}}
The average for the first 5 tests can be calculated as
{{{(260+x)/5}}}
and since the average is 66%,
{{{(260+x)/5=66}}} --> {{{260+x=66*5}}} --> {{{260+x=330}}} --> {{{x=330-260}}} --> {{{highlight(x=70)}}}