Question 1121728
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To solve the problem, you must have all dimensions in uniform / consistent units.


In this case, inches are preferred units.


Also, you need to know that 1 foot = 12 inches.



<pre>
    Let x be the mother height, in inches.

    Then Susan's height is (x+3) inches.


    Susan' sister is {{{2}}}{{{1/3}}} feet shorter than Susan.


    {{{2}}}{{{1/3}}} feet = {{{24 + 12/3}}} inches = 24 + 4 inches = 28 inches.


    Hence, as the condition states, the Susan's sister is 28 inches shorter than Susan.


    In other words, Susan's sister height is ((x+3) - 28) = (x-25) inches.


    The equation, from the condition, is


        x - 25 = (8/13)*x.


    ============>  13x - 13*25 = 8x  ====>  13x - 8x = 13*25  ====>  5x = 13*25  ====>  x = 13*5 = 65 inches = 5 ft and 5 inches.


    <U>Answer</U>.  The mother's height is 5 ft and 5 inches.
</pre>

Solved.