Question 1183712
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5 years back the ratio of kate and sharon 4:3. 
In 5 years, the sum of the ages of Kate and Sharon will be 90. 
How old is Sharon right now?
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<pre>
In his post, @josgarithmetic writes equation 

    {{{(90-x-5)/(x-5)}}} = {{{4/3}}}


and states that it can be easily solved.


I tried to follow his instruction

    3*(90-x-5) = 4*(x-5)

    270 - 3x - 15 = 4x - 20

    270 - 15 + 20 = 4x + 3x

         275      = 7x

          x       = {{{275/7}}} = 39 {{{2/7}}}.


Notice that this value even is not integer.

@josgarithmetic does not declare what his unknown  " x "  is.

But it is clear that  NEITHER Kate age  NOR Sharon age  is  non-integer number in this problem.


    +------------------------------------------------------------------------------------------+
    |                 You may ask: WHAT IS THE MATTER ?                                        |
    |                                                                                          |
    |                                                                                          |
    |  The matter is that this @josgarithmetic's setup equation is  <U>I N C O R R E C T</U>.         |
    |                                                                                          |                                                                                        |
    |    In other words (to make my statement even more clear), it is  <U>W R O N G</U>.              |
    +------------------------------------------------------------------------------------------+


    Unfortunately, tutor @greenestamps MISSED this error and declared the @josgarithmetic's setup as "fine",  instead.



        THEREFORE, I came to prevent this huge mistake considering the WRONG setup as a correct.


                      +-------------------------------------------+
                      |   The correct setup would be AS FOLLOWS   |
                      +-------------------------------------------+


Let x be the Sharon present age.

Then 5 years ago Sharon's age was (x-5) years.


The Kate's age in 5 years will be  90 - (x+5);

hence, the Kate's age 5 years back was  (90 - (x+5) - 10) = 80-(x+5) years.


Now we can write equation describing the ratio of their ages 5 years back


    {{{(80-(x+5))/(x-5)}}} = {{{4/3}}}.


Now we can solve it, first cross-multiplying


    3*(80-(x+5)) = 4*(x-5)

    240 - 3x - 15 = 4x - 20

    240 - 15 + 20 = 4x + 3x

         245      = 7x

          x       = 245/7 = 35.


<U>ANSWER</U>.  The Sharon's present age is 35 years.


<U>CHECK</U>.   In 5 years, Sharon will be 35+5 = 40 years old;  Kate will be 90-40 = 50 years old; hence, Kate is 45 years old now.

         5 years ago, Sharon was 35-5 = 30 years old, while Kate was 45-5 = 40 years old, and the ratio of their ages 5 years ago was really  {{{40/30}}} = {{{4/3}}}.

         The check  <U>confirms</U> that my solution is correct.
</pre>

Solved.