SOLUTION: If Beth gets a 97 on her next math test, her average will be 90. If she gets 73, her average will be 87. How many tests has Beth already taken?

Question 251983: If Beth gets a 97 on her next math test, her average will be 90. If she gets 73, her average will be 87. How many tests has Beth already taken?
Found 2 solutions by hitokiri15, palanisamy:
Answer by hitokiri15(3) (Show Source): You can put this solution on YOUR website!
"Word Problems Involving Products and Factoring"
Find two consecutive positive numbers such that the product of the sum and difference of the numbers plus 8 is the sum of their squares. can you solve this pls=( tyty so much
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
First method
Let the total number of tests taken by Beth be x.
If Beth gets a 97 on her next math test, her average will be 90
If she gets 73, her average will be 87.
As of now, 90x - 97 = 87x-73
90x-87x = 97-73
3x = 24
x = 8
So, the number of tests already undertaken = 8-1 = 7
Second Method
Let the number of tests already undertaken be x and
the total marks secured be n.
If Beth gets a 97 on her next math test, her average will be 90
(n+97)/(x+1) = 90
n+97 = 90(x+1)
n+97 = 90x+90
n+7 = 90x ......(1)
Next,
If she gets 73 in the next test, her average will be 87
(n+73)/(x+1) = 87
n+73 = 87(x+1)
n+73 = 87x+87
n = 87x + 14 ......(2)
(1)-(2):
7 = 3x-14
21 = 3x
7 = x
So, the number of tests already undertaken = 7

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