Problem:
Points B and C lie on AD. The length of AB is 4 times the length of BD, and the length of AC is 9 times the length of CD. The length of BC is what fraction of the length of AD?
Answer Choices:
A. 361
B. 131
C. 101
D. 365
E. 51
Solution:
Because AB+BD=AD and AB=4BD, it follows that BD=51⋅AD. By similar reasoning, CD=101⋅AD. Thus
BC=BD−CD=51⋅AD−101⋅AD=(C)101⋅AD
The problems on this page are the property of the MAA's American Mathematics Competitions