Difference between revisions of "2006 AMC 12A Problems/Problem 5"
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== Problem == | == Problem == | ||
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Doug and Dave shared a pizza with <math>8</math> equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was <math>8</math> dollars, and there was an additional cost of <math>2</math> dollars 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? | Doug and Dave shared a pizza with <math>8</math> equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was <math>8</math> dollars, and there was an additional cost of <math>2</math> dollars 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? | ||
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== Solution == | == Solution == | ||
| − | + | Dave and Doug paid <math>8+2=10</math> dollars in total. Doug paid for three slices of plain pizza, which cost <math>\frac{3}{8}\cdot 8=3</math>. Dave paid <math>10-3=7</math> dollars. Dave paid <math>7-3=4</math> more dollars than Doug. The answer is <math>\mathrm{(D)}</math>. | |
| − | Dave and Doug paid <math>8+2=10</math> dollars in total. Doug paid for three slices of plain pizza, which cost <math>\frac{3}{8}\cdot 8=3</math>. Dave paid <math>10-3=7</math> dollars. Dave paid <math>7-3=4</math> more dollars than Doug. The answer is D. | ||
== See also == | == See also == | ||
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{{AMC12 box|year=2006|ab=A|num-b=4|num-a=6}} | {{AMC12 box|year=2006|ab=A|num-b=4|num-a=6}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 23:34, 27 April 2008
Problem
Doug and Dave shared a pizza with 
equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was dollars, and there was an additional cost of 
dollars 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?
Solution
Dave and Doug paid 
dollars in total. Doug paid for three slices of plain pizza, which cost 
. Dave paid 
dollars. Dave paid 
more dollars than Doug. The answer is 
.
See also
| 2006 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
