geometry
posted by james .
B is the midpoint of AC, D is the midpoint of CE, and Bd=14. find AE.
B is the midpoint of AC, D is the midpoint of CE and BD=7. Find AE.

Just lay out the points on the line
BD contains the right half of BC and the left half of CE
So, what's left is the same length: The left half of AC and the right half of CE
AE = AB + BC + CD + DE
but BD = BC + CD = 14
so,
AE = AB + 14 + DE
However,
AB = BC and CD = DE so AB+DE = BC+CD = 14
AE = 14 + 14 = 28
With that in hand, the 2nd problem should be trivial.