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On a number line, the coordinate of point X is $-18\frac{1}{2}$ and the coordinate of point Y is $25\frac{1}{3}$. What mixed number corresponds to the coordinate of point Z if the distance between X and Z is one-third of the distance between Z and Y ?

 Sep 23, 2023
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the coordinate of point x is -18 1/2

the coordinate of point is y is 25 1/3


X______________________________________________Y

-18 1/2.......................................................................................................25 1/3

the distance between X and Z is one-third of the distance between Z and

X______d______Z_____________3d_______________Y

-18 1/2......................................................................................................25 1/3

the distance between X and Y

d = the distance between and Y divided by 4

d = (25 1/3 + 18 1/2)/4

d = 263/24

3d = (3 * 263)/24 = 263/8

the coordinate of the point Z is -18 1/2 + 263/24 = -181/24 = -7 13/24

or 

25 1/3 - 263/8 = -181/24 = -713/24

answer: the coordinate of the point Z is -7 13/24

 Sep 27, 2023

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