Difference between revisions of "2005 AMC 10A Problems/Problem 1"

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==Problem==
 
==Problem==
While eating out, Mike and Joe each tipped their server <math>\$2</math>. Mike tipped <math>10%</math> of his bll and Joe tipped <math>20%</math> of his bill. What was the difference, in dollars between their bills?  
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While eating out, Mike and Joe each tipped their server <math>\</math>2<math>. Mike tipped </math>10%<math> of his bill and Joe tipped </math>20%<math> of his bill. What was the difference, in dollars between their bills?  
  
<math> \mathrm{(A) \ } 2\qquad \mathrm{(B) \ } 4\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 20 </math>
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</math> \mathrm{(A) \ } 2\qquad \mathrm{(B) \ } 4\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 20 $
  
 
==Solution==
 
==Solution==

Revision as of 15:33, 24 December 2009

Problem

While eating out, Mike and Joe each tipped their server $$2$. Mike tipped$10%$of his bill and Joe tipped$20%$of his bill. What was the difference, in dollars between their bills?$ \mathrm{(A) \ } 2\qquad \mathrm{(B) \ } 4\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 20 $

Solution

Let $m$ be Mike's bill and $j$ be Joe's bill.

$\frac{10}{100}m=2$

$m=20$

$\frac{20}{100}j=2$

$j=10$

So the desired difference is $m-j=20-10=10 \Rightarrow D$

See Also