SOLUTION: Peter and Diane have the same average in mathematics. On the next test, Diane scored 97% and her average improved to 90%, but Peter scored 73%, and his average decreased to 87%. Ho

Algebra ->  Statistics  -> Describing-distributions-with-numbers -> SOLUTION: Peter and Diane have the same average in mathematics. On the next test, Diane scored 97% and her average improved to 90%, but Peter scored 73%, and his average decreased to 87%. Ho      Log On


   

Question 1122734: Peter and Diane have the same average in mathematics. On the next test, Diane scored 97% and her average improved to 90%, but Peter scored 73%, and his average decreased to 87%. How many tests had preceded this last test?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Peter and Diane have the same average in mathematics.
On the next test, Diane scored 97% and her average improved to 90%,
but Peter scored 73%, and his average decreased to 87%.
How many tests had preceded this last test?
:
let a = the average of the previous tests
let x = no. of previous tests
then
xa = the total of previous tests
:
Write an equation for each person
%28%28xa%2B97%29%29%2F%28x%2B1%29 = 90
xa + 97 = 90(x+1)
and
%28%28xa%2B73%29%29%2F%28x%2B1%29 = 87
xa + 73 = 87(x+1)
Using elimination
xa + 97 = 90(x+1)
xa + 73 = 87(x+1)
---------------subtraction eliminates xa
0 + 24 = 3(x+1)
24 = 3x + 3
24 - 3 = 3x
21 = 3x
x = 21/3
x = 7 tests previously