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2006 AMC 10A 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?

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Solution

Each of the 88 slices costs $1.\$1. Dave ate 55 slices and also pays the extra $2\$2 for the anchovies, for a total of 5+2=75 + 2 = 7 dollars. Doug ate 33 slices, paying 33 dollars. So Dave paid 73=47 - 3 = 4 dollars more. Thus, the correct answer is D.

More practice

Concepts: money · fraction

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