2006 AMC 12A Problem 5

Question

Doug and Dave shared a pizza with

8

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,

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 then paid for what he had eaten. How many more dollars did Dave pay than Doug?

1

2

3

4

5

Answer: D

Concepts:fraction money

Difficulty rating: 1190

Small hint:

The plain pizza is

\$8

for

8

slices, so each plain slice costs

\$1

Big hint:

Spread the

\$2

anchovy surcharge over the

4

anchovy slices, then total each person’s cost

Solution:

Each plain slice costs

\$1.

The

\$2

anchovy charge is spread over the

4

anchovy slices, adding

\$0.50

each, so an anchovy slice costs

\$1.50.

Dave ate

4

anchovy slices and

1

plain slice:

4\cdot 1.5 + 1 = \$7.

Doug ate the

3

remaining plain slices:

\$3.

Dave paid

7 - 3 = \$4

more.

Thus, the correct answer is D.