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2006 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

Doug and Dave shared a pizza with 88 equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half of the pizza. The cost of a plain pizza was $8,\$8, and there was an additional cost of $2\$2 for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each then paid for what he had eaten. How many more dollars did Dave pay than Doug?

Answer choices

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Solution

Each plain slice costs $1.\$1. The $2\$2 anchovy charge is spread over the 44 anchovy slices, adding $0.50\$0.50 each, so an anchovy slice costs $1.50.\$1.50. Dave ate 44 anchovy slices and 11 plain slice: 41.5+1=$7.4\cdot 1.5 + 1 = \$7. Doug ate the 33 remaining plain slices: $3.\$3. Dave paid 73=$47 - 3 = \$4 more. Thus, the correct answer is D.

More practice

Concepts: fraction · money

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.