Difference between revisions of "2006 AMC 10A Problems/Problem 5"
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== Problem == | == Problem == | ||
| − | 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 | + | 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 of 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? |
<math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 3\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } 5 </math> | <math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 3\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } 5 </math> | ||
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== Solution == | == Solution == | ||
Since Doug did not eat any of the anchovy part, Dave already has to pay $2 dollars. Dave ate half+1 slice of the pizza, or <math>\frac{5}{8}</math> of it. Thus, he had to pay <math>\frac{5}{8}</math> of the price and paid $5. Doug ate <math>\frac{3}{8}</math> and paid $3. Thus, Dave paid $7 overall and Doug, $3. Our answer is | Since Doug did not eat any of the anchovy part, Dave already has to pay $2 dollars. Dave ate half+1 slice of the pizza, or <math>\frac{5}{8}</math> of it. Thus, he had to pay <math>\frac{5}{8}</math> of the price and paid $5. Doug ate <math>\frac{3}{8}</math> and paid $3. Thus, Dave paid $7 overall and Doug, $3. Our answer is | ||
Revision as of 08:39, 28 July 2006
Problem
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 of 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?
Solution
Since Doug did not eat any of the anchovy part, Dave already has to pay $2 dollars. Dave ate half+1 slice of the pizza, or 
of it. Thus, he had to pay of the price and paid $5. Doug ate 
and paid $3. Thus, Dave paid $7 overall and Doug, $3. Our answer is
