The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
In this problem we have that
UV+VW+WX=UX -----> by addition segment postulate
we have
UX=8 units
so
UV+VW+WX=8 -------> equation A
UV/VW=1/3 ------> equation B
UV/WX=1/4 -----> equation C
Solve the system of equations
In equation B isolate the variable VW
so
3UV=VW
VW=3UV -------> equation D
In equation C isolate the variable WX
4UV=WX
WX=4UV ------> equation E
Substitute equation D and equation E in equation A
UV+(3UV)+(4UV)=8
solve for UV
8UV=8
UV=1
Find VW
VW=3UV
VW=3(1)=3 units
FInd WX
WX=4UV
WX=4(1)=4 units
Find out the value of VX
we have that
VX=VW+WX
substitute
VX=3+4=7 units
therefore
VX=7