2006 AMC 12A Problems/Problem 5

Revision as of 13:56, 12 July 2006 by Matt276eagles (talk | contribs) (Solution)

Problem

Doug and Dave shared a pizza with $8$ equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was $8$, and there was an additional cost of $2$ for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each paid for what he had eaten. How many more dollars did Dave pay than Doug?

$\mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 3\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ }  5$

Solution

Each slice of plain pizza costs $\frac{1}{8}\cdot 8=1$ dollar. Each slice of anchovy pizza costs $1+\frac{1}{4}\cdot 2=\frac{3}{2}$ dollars. Dave paid $4\cdot\frac{3}{2}+1\cdot 1=7$ dollars, and Doug paid $3\cdot 1=3$ dollars. Dave paid $7-3=4$ dollars than Doug. The answer is D.

See also