8
Part of 2015 AMC 10
Problems(2)
Pete and Claire and Ages... Oh My!
Source: 2015 AMC 12A #6/10A #8
2/4/2015
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be ?
ratioAMC
Transformations of F
Source: 2015 AMC 10B #8
2/26/2015
The letter F shown below is rotated clockwise around the origin, then reflected in the -axis, and then rotated a half turn around the origin. What is the final image?
[asy]
import cse5;pathpen=black;pointpen=black;
size(2cm);
D((0,-2)--MP("y",(0,7),N));
D((-3,0)--MP("x",(5,0),E));
D((1,0)--(1,2)--(2,2)--(2,3)--(1,3)--(1,4)--(3,4)--(3,5)--(0,5));
[/asy][asy]
import cse5;pathpen=black;pointpen=black;
unitsize(0.2cm);
D((0,-2)--MP("y",(0,7),N));
D(MP("(A) ",(-3,0),W)--MP("x",(5,0),E));
D((1,0)--(1,2)--(2,2)--(2,3)--(1,3)--(1,4)--(3,4)--(3,5)--(0,5));
//
D((18,-2)--MP("y",(18,7),N));
D(MP("(B) ",(13,0),W)--MP("x",(21,0),E));
D((17,0)--(17,2)--(16,2)--(16,3)--(17,3)--(17,4)--(15,4)--(15,5)--(18,5));
//
D((36,-2)--MP("y",(36,7),N));
D(MP("(C) ",(29,0),W)--MP("x",(38,0),E));
D((31,0)--(31,1)--(33,1)--(33,2)--(34,2)--(34,1)--(35,1)--(35,3)--(36,3));
//
D((0,-17)--MP("y",(0,-8),N));
D(MP("(D) ",(-3,-15),W)--MP("x",(5,-15),E));
D((3,-15)--(3,-14)--(1,-14)--(1,-13)--(2,-13)--(2,-12)--(1,-12)--(1,-10)--(0,-10));
//
D((15,-17)--MP("y",(15,-8),N));
D(MP("(E) ",(13,-15),W)--MP("x",(22,-15),E));
D((15,-14)--(17,-14)--(17,-13)--(18,-13)--(18,-14)--(19,-14)--(19,-12)--(20,-12)--(20,-15));
[/asy]
rotationAsymptoteAMCUSA(J)MOUSAJMOAIME