<PRE><B>Question 585559</B>
Jay realizes he needs a mark of 100% on his next test in order to achieve a 90% average for all his tests.
However if he gets a mark of 70% on the next test,his average will be 87%.
After he writes the next test,how many tests will he have written?
:
Let n = total number of tests
Let a = average of the test already taken
:
Get 100 on the last test equation
{{{((a(n-1)+100))/n}}} = 90
a(n-1) + 100 = 90n
:
Get 70 on the last test equation
{{{((a(n-1)+70))/n}}} = 87
a(n-1) + 70 = 87n
:
Use elimination here
a(n-1) + 100 = 90n
a(n-1) +  70 = 87n
--------------------subtraction eliminates a(n-1), find n
0 + 30 = 3n
n = 10 total tests taken
:
:
If you wish to prove this to yourself, solve for a in one of the equations, then check the average in the other equation
9a + 100 = 90(10)</PRE>