<PRE><B>Question 1122734</B>
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
{{{((xa+97))/(x+1)}}} = 90
xa + 97 = 90(x+1)
and
{{{((xa+73))/(x+1)}}} = 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 </PRE>