SOLUTION: I need help with this application problem. If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting faction is equivalent to the r

Algebra ->  Expressions-with-variables -> SOLUTION: I need help with this application problem. If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting faction is equivalent to the r      Log On


   

Question 1147723: I need help with this application problem.
If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting faction is equivalent to the reciprocal of 2/3. What is the number?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

The equation is


    %2823%2Bx%29%2F%2812-x%29 = 3%2F2.


Cross multiply


    2*(23+x) = 3*(12-x)

    46 + 2x = 36 - 3x

    2x + 3x = 36 - 46

    5x        = -10

     x        = -10/5 = -2.


ANSWER.  The number is -2.

You can easily check it on your own.


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