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
Algebra ->
Average
-> 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
Log On
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?
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
