Question 1208620
.
On the number line x= 2/9 and y= 17/18. The point z divides the segment from x to y into two parts such that 
the distance from x to z is 5/9 of the distance from z to y. Find the distance from z to y.
~~~~~~~~~~~~~~~~~~


<pre>
As you read the problem, write this equation

    {{{z - 2/9}}} = {{{(5/9)*(17/18-z)}}}.


This equation is the literal translation of the words to Math.

To solve, multiply both sides by 9.  You will get

    9z - 2 = {{{5*(17/18-z)}}}.


Multiply both parts of the last equation by 18.  You will get

    162z - 36 = 5*17 - 5*18z,

    162z - 36 = 85 - 90z,

    162z + 90z = 85 + 36,

    252z = 121,

       z = {{{121/252}}}.


The distance from z to y is  {{{17/18 - 121/252}}} = {{{(14*17)/252 - 121/252}}} = {{{(14*17-121)/252}}} = {{{117/252}}} = {{{13/28}}}.


<U>ANSWER</U>.  The distance from z to y is  {{{13/28}}}.
</pre>

Solved.