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If John gets a 97 on his next math test, his average will be 90. If he gets73, his...

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christiano-cr7 | Salutatorian

Posted September 21, 2013 at 5:34 AM via web

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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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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 21, 2013 at 5:54 AM (Answer #1)

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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.

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