SOLUTION: When toni got a grade of 98 on a certain test it raised her test average by one point. But when she got a grade of 70 on her next test, her average went down by two points. How man

Question 533052: When toni got a grade of 98 on a certain test it raised her test average by one point. But when she got a grade of 70 on her next test, her average went down by two points. How many tests did she take?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
When toni got a grade of 98 on a certain test it raised her test average by one point.
But when she got a grade of 70 on her next test, her average went down by two points.
How many tests did she take?
:
let n = original number of test, before the 98 test
let a = original average of these tests
:
"When toni got a grade of 98 on a certain test it raised her test average by one point."
a + 1 =
Multiply both sides by (n+1)
(n+1)(a+1) = na + 98
FOIL
na + n + a + 1 = na + 98
subtract na from both sides
n + a + 1 = 98
subtract 1 from both sides, a simple two unknown equation:
n + a = 97
:
Note that now her average is (a+1) and the number of test taken is (n+1)
:
" But when she got a grade of 70 on her next test, her average went down by two points."
Now her average is (a+1-2) and the number of test taken is n+2
a + 1 - 2 =
a - 1 =
multiply both sides by (n+2)
(n+2)(a-1) = na + 168
FOIL
na - n + 2a - 2 = na + 168
Subtract na and add 2 to both sides
-n + 2a = 170
:
Use elimination here on these two equations
-n + 2a = 170
+n + a = 97
---------------adding eliminates n, find a
3a = 267
a =
a = 89 is original average before the two test
:
Find n
n + 89 = 97
n = 97 - 89
n = 8 test taken originally, then a total of 10 test were taken by Toni
:
:
See if that works
= 88 is the final average which is 1 point below the original average of 89
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