SOLUTION: 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 d

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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.
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~ 

As you read the problem, write this equation

     = .


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

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

    9z - 2 = .


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 = .


The distance from z to y is   =  =  =  = .


ANSWER.  The distance from z to y is  .

Solved.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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.

To keep things uniform, let's change x to match y's denominator, 18. We than get x as:  
Distance between x and y:  
With point z between xy, we get segments, xz, and zy, with xz + zy = xy ===> xz = xy - zy 
As distance from x to z is  the distance from z to y, 
                                                     -- Substituting xy - zy for xz 
                                                     ----- Substituting  for xy
                                                  13 - 18zy = 10zy ----- Multiplying by LCD, 18
                                                         13 = 10zy + 18zy
                                                         13 = 28zy
                          Distance from z to y, or 

It would seem a lot less complex - if it's considered so now - to draw a number line in 18s,
i.e. , and marking off points x, y, and z, so this can be clearer to you.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The distance from x to z is 5/9 of the distance from z to y.

That means the total distance from x to y is divided in two parts in the ratio 5:9. So the distance from x to z is 5/14 of the total distance from x to y and the distance from z to y is 9/14 of the total distance from x to y.

The distance from x to y is 17/18 - 2/9 = 17/18 - 4/18 = 13/18.

So the distance from y to z is (9/14) of (13/18):



ANSWER: 13/28
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