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

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)   (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)   (Show Source): You can put this solution on YOUR website!
Question, find distance from z to y. ~~This would be 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. "

~~Simplify and compute this.~~
Answer by ikleyn(52824)   (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 = = = . 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 - . 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 - = . +-------------------------------------------+ | 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 . ANSWER

Solved.

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

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