SOLUTION: Jay realizes he needs a mark of 100% on his next test in order to achive a 90%average for all his tests.However if he gets a mark of 70% on the next test,his average will be 87%.Af

Algebra ->  Probability-and-statistics -> SOLUTION: Jay realizes he needs a mark of 100% on his next test in order to achive a 90%average for all his tests.However if he gets a mark of 70% on the next test,his average will be 87%.Af      Log On


   

Question 585559: Jay realizes he needs a mark of 100% on his next test in order to achive 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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
%28%28a%28n-1%29%2B100%29%29%2Fn = 90
a(n-1) + 100 = 90n
:
Get 70 on the last test equation
%28%28a%28n-1%29%2B70%29%29%2Fn = 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)