Points X and Z are on a number line, and point Y partitions line XZ into two parts so that the ratio of the length of line segment XY to the length of line segment YZ is 3:5. The coordinate of X is 0.4, and the coordinate of Y is 2.7. What is the coordinate of Z? Show all work.

Answer 1

3 + 5 = 8
so ratio of xz to xy is 8/3
but xy is 2.7 - 0.4 = 2.3
so xz = (8/3)2.3 = 6.13
so z is at 0.4 + 6.13 = 6.53

Answer 2

XY/YZ = 3/5
(2.7-0.4)/YZ = 3/5
YZ = 3.83
Z = Y + 3.83 = 2.7 + 3.83 = 6.53