AMC 8 2003 Problem 9
Source:
July 23, 2011
geometrytrapezoidrectangleparallelogramAMC 8
Problem Statement
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies di ffer, as shown. Art's cookies are trapezoids:
[asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
draw(origin--(5,0)--(5,3)--(2,3)--cycle);
draw(rightanglemark((5,3), (5,0), origin));
label("5 in", (2.5,0), S);
label("3 in", (5,1.5), E);
label("3 in", (3.5,3), N);[/asy] Roger's cookies are rectangles:
[asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
draw(origin--(4,0)--(4,2)--(0,2)--cycle);
draw(rightanglemark((4,2), (4,0), origin));
draw(rightanglemark((0,2), origin, (4,0)));
label("4 in", (2,0), S);
label("2 in", (4,1), E);[/asy] Paul's cookies are parallelograms:
[asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
draw(origin--(3,0)--(2.5,2)--(-0.5,2)--cycle);
draw((2.5,2)--(2.5,0), dashed);
draw(rightanglemark((2.5,2),(2.5,0), origin));
label("3 in", (1.5,0), S);
label("2 in", (2.5,1), W);[/asy] Trisha's cookies are triangles:
[asy]size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
draw(origin--(3,0)--(3,4)--cycle);
draw(rightanglemark((3,4),(3,0), origin));
label("3 in", (1.5,0), S);
label("4 in", (3,2), E);[/asy]Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Art's cookies sell for 60 cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?