SOLUTION: on the number line x=2/5 and y=11/5 the point z divides the segment from x to y into two parts such that the distance from x to z is 2/3 of the distance from z to y. find the dista

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Question 1100326: on the number line x=2/5 and y=11/5 the point z divides the segment from x to y into two parts such that the distance from x to z is 2/3 of the distance from z to y. find the distance from z to y
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
(removed )


-
-
x to z,
z to y,

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distance from x to z is 2/3 of the distance from z to y
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---
CHECK:




-------checks right
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Obviously the other tutor had a typo in her final answer; 2/5 plus 6/5 is 8/5, not 7/5.

But she also misread the problem. Her answer has z two-thirds of the distance from x to y.

But the problem says the distance from x to z is 2/3 of the distance from z to y.
That means that z is 2/5 of the distance from x to z -- not 2/3 of the distance.

The distance from x to y is 9/5. The distance from x to z is 2/5 of that distance; the distance from z to y is 3/5 of that distance.

The problem asked for the distance from z to y; that distance is
Answer by ikleyn(52793)   (Show Source): You can put this solution on YOUR website!
.

     x        a         z                b                  y
-----|------------------|-----------------------------------|-----

                                                          

In this picture I showed the number line by (-------),  the points x =   and  y =   and  the point z,  whose position is under the question.


I also denoted by "a" the distance from x to z  and by "b" the distance from z to y.

We are given that   = ,  and the problem asks to find  b.


We have these two equations 

a + b =  -  = ,      (1)      and

 = .                    (2)

From (2),  a = .   Substitute it into (1).  You will get

 + b = ,  which is equivalent to

 = .

It implies  b =  = .

Answer.  The distance from z to y is   .

===============
In his solution, @josgarithmetic outputted the value of the coordinate of the point z, although the problem asked for the distance from z to y.

It is the source of the difference between his answer and the answers by the tutor @greenestamps and mine.



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