If John gets a 97 on his next math test, his average will be 90. If he gets

73, his average will be 87. How many tests has John already taken?

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Let us say John has taken already X number of tests and his current average for the X tests taken is A.

If John gets a 97 on his next math test, his average will be 90.

So we can say;

`(AxxX+97)/(X+1) = 90`

`AxxX+97 = 90(X+1)`

`AxxX = 90(X+1)-97 ----(1)`

If he gets 73, his average will be 87.

Now we can say;

`(AxxX+73)/(X+1) = 87`

`AxxX+73 = 87(X+1)`

`AxxX = 87(X+1)-73 ----(2)`

(1) = (2)

`90(X+1)-97 = 87(X+1)-73`

`X = 21/3 `

`X = 7`

*So John has already taken 7 subjects.*

If John gets a 97 on his next math test, his average will be 90. If he gets

73, his average will be 87.

Let the number of test John has already taken be n and let his average in these tests be a.

If he get 97 in the next test, the new average is (n*a + 97)/(n+1) = 90

And if he gets 90, the new average is (n*a + 73)/(n+1) = 87

From (n*a + 97)/(n+1) = 90, n*a = 90n + 90 - 97 = 90n - 7

Substitute this in (n*a + 73)/(n+1) = 87

(90n - 7+ 73)/(n+1) = 87

90n + 66 = 87n + 87

3n = 21

n = 7

John has taken 7 tests already.

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