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

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==Problem==
 
==Problem==
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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>2</math> dollars. 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?  
  
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<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> \textbf{(A) } 2\qquad \textbf{(B) } 4\qquad \textbf{(C) } 5\qquad \textbf{(D) } 10\qquad \textbf{(E) } 20 </math>
  
 
==Solution==
 
==Solution==
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<math>j=10</math>
 
<math>j=10</math>
  
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So the desired difference is <math>m-j=20-10=10 \Rightarrow D</math>
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So the desired difference is <math>m-j=20-10=10 \Rightarrow \boxed{\textbf{(D) }10}</math>
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==Video Solution==
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CHECK OUT: Video Solution:
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https://youtu.be/OT47ZnF5MPY
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==Video Solution 2==
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https://youtu.be/mApPRP9v_XE
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~Charles3829
  
 
==See Also==
 
==See Also==
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*[[2005 AMC 10A Problems]]
 
  
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*[[2005 AMC 10A Problems/Problem 2|Next Problem]]
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{{AMC10 box|year=2005|ab=A|before=First Problem|num-a=2}}
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[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 18:05, 25 December 2022

Problem

While eating out, Mike and Joe each tipped their server $2$ dollars. Mike tipped $10\%$ of his bill and Joe tipped $20\%$ of his bill. What was the difference, in dollars between their bills?

$\textbf{(A) } 2\qquad \textbf{(B) } 4\qquad \textbf{(C) } 5\qquad \textbf{(D) } 10\qquad \textbf{(E) } 20$

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 $m-j=20-10=10 \Rightarrow \boxed{\textbf{(D) }10}$

Video Solution

CHECK OUT: Video Solution: https://youtu.be/OT47ZnF5MPY

Video Solution 2

https://youtu.be/mApPRP9v_XE

~Charles3829

See Also

2005 AMC 10A (Problems • Answer Key • Resources)
Preceded by
First Problem 		Followed by
Problem 2
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 10 Problems and Solutions

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