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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
(removed )


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x to z, z-2%2F5
z to y, 11%2F5-z

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distance from x to z is 2/3 of the distance from z to y
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highlight_green%28z-2%2F5=%282%2F3%29%2811%2F5-z%29%29

z-2%2F5=22%2F15-2z%2F3
15z-6=22-%282z%2F3%29%2815%29
15z-6=22-10z
25z=28
highlight%28z=28%2F25%29

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CHECK:
28%2F25-2%2F5=%282%2F3%29%2811%2F5-28%2F25%29
28%2F25-10%2F25=%282%2F3%29%2855%2F25-28%2F25%29
18%2F25=%282%2F3%29%2827%2F25%29
18%2F25=%282%2A9%29%2F25
18%2F25=18%2F25-------checks right

Answer by greenestamps(13200) About Me  (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 %283%2F5%29%2A%289%2F5%29+=+27%2F25

Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.

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

     2%2F5                                                     11%2F5

In this picture I showed the number line by (-------),  the points x = 2%2F5  and  y = 11%2F5  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  a%2Fb = 2%2F3,  and the problem asks to find  b.


We have these two equations 

a + b = 11%2F5 - 2%2F5 = 9%2F5,      (1)      and

a%2Fb = 2%2F3.                    (2)

From (2),  a = %282%2F3%29%2Ab.   Substitute it into (1).  You will get

%282%2F3%29%2Ab + b = 9%2F5,  which is equivalent to

%285%2F3%29%2Ab = 9%2F5.

It implies  b = %289%2F5%29%2A%283%2F5%29 = 27%2F25.

Answer.  The distance from z to y is   27%2F25.

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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.