SOLUTION: 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

Algebra ->  Graphs -> SOLUTION: 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      Log On


   

Question 1197224: 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.
Found 3 solutions by Theo, josgarithmetic, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

x = 1/4
y = 11/12
z - x = 3/8 * (y-z) = 3/8 * y = 3/8 * z
add 3/8 * z to both sides of the equation to get:
z - x + 3/8 * z = 3/8 * y
add x to both sides of the equation to get:
z + 3/8 * z = 3/8 * y + x
combine like terms to get:
11/8 * z = 3/8 * y + x
since x = 1/4 and y = 11/12, then:
11/8 * z = 3/8 * 11/12 + 1/4 = 33/96 + 24/96 = 57/96
solve for z to get:
z = 57/96 * 8/11 = 456/1056.
y - z = 11/12 - 456/1056 = 968/1056 - 456/1056 = 512/1056 = 16/33.

since the distance from x to z is 3/8 * the distance from z to y, then the distance from x to z = 3/8 * 16/33 = 48/264.
the distance from x to y is therefore 48/264 + 16/33 = 48/264 + 128/264 = 176/264.
y minus x = 11/12 - 1/4 = 11/12 - 3/12 = 8/12 = 176/264.
the two ways of calculating the distance between x and y are the same, confirming the arithmetic was correct.

your solution is that the distance from z to y is equal to 16/33.

let me know if you have any questions.
theo

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Question, find distance from z to y. This would be 5%2F8 of the distance between x and y. Think about that. When it makes sense, then....

MISREAD THIS PART:
",... such that the distance from x to z is 3/8 of the distance from z to y. "

cross%28%285%2F8%29%2811%2F12-1%2F4%29%29
Simplify and compute this.

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~ 

The distance between the given points x = 1/4 and y = 11/12 is

    11%2F12+-+1%2F4 = 11%2F12+-+3%2F12 = 8%2F12 = 2%2F3.


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%2F3 - 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%2F3 - d = %283%2F8%29%2Ad.


      +-------------------------------------------+
      |    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%2F33.    ANSWER

Solved.


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