MathDB

4

Part of 2009 AIME Problems

Problems(2)

Parallelogram

Source: AIME 2009I Problem 4

3/18/2009
In parallelogram ABCD ABCD, point M M is on AB‾ \overline{AB} so that \frac{AM}{AB} \equal{} \frac{17}{1000} and point N N is on AD‾ \overline{AD} so that \frac{AN}{AD} \equal{} \frac{17}{2009}. Let P P be the point of intersection of AC‾ \overline{AC} and MN‾ \overline{MN}. Find ACAP \frac{AC}{AP}.
geometryparallelogramratioAMCAIMErectangleanalytic geometry
Grape-Eating Contest

Source: AIME 2009II Problem 4

4/2/2009
A group of children held a grape-eating contest. When the contest was over, the winner had eaten n n grapes, and the child in k kth place had eaten n\plus{}2\minus{}2k grapes. The total number of grapes eaten in the contest was 2009 2009. Find the smallest possible value of n n.
calculusderivativeAMCAIME