Question 1197224
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On the number line x = 1/4 and y = 11/12. 
The point z divides the segment from x to y into two parts such that the distance 
from x to z is 3/8 of the distance from z to y. Find the distance from z to y.
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<pre>
The distance between the given points x = 1/4 and y = 11/12 is

    {{{11/12 - 1/4}}} = {{{11/12 - 3/12}}} = {{{8/12}}} = {{{2/3}}}.


From the problem's description, point z is located BETWEEN points x and y.


    +---------------------------------------------------------+
    |   Let d be the distance from z to y: it is precisely    |
    |   the unknown quantity under the problem's question.    |
    +---------------------------------------------------------+


Then the distance from x to z is  {{{2/3}}} - {{{d}}}.


You are given that 

    the distance from x to z is 3/8 of the distance from z to y.


In mathematical terms, it means that

    {{{2/3}}} - {{{d}}} = {{{(3/8)*d}}}.


      +-------------------------------------------+
      |    Thus you just have an equation for d   |
      |        to solve it and to find d.         |
      +-------------------------------------------+


Multiply both sides by 24 to rid of the denominators. You will get then

    2*8 - 24d = 3*3*d

    16        = 9d + 24d

    16        = 33d

     d        = 16/33.


Thus the distance d from  z to y is  {{{16/33}}}.    <U>ANSWER</U>
</pre>

Solved.



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Ignore the post by &nbsp;@josgarithmetic, &nbsp;since his &nbsp;" solution " &nbsp;and his instructions are &nbsp;TOTALLY &nbsp;WRONG.