2005 AMC 10A Problems/Problem 1: Difference between revisions
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While eating out, Mike and Joe each tipped their server <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? | While eating out, Mike and Joe each tipped their server <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> \ | <math>\textbf{(A) } 2\qquad \textbf{(B) } 4\qquad \textbf{(C) } 5\qquad \textbf{(D) } 10\qquad \textbf{(E) } 20 </math> | ||
==Solution== | ==Solution== | ||
Let <math>m</math> be Mike's bill and <math>j</math> be Joe's bill (both in dollars). We then have <math>\frac{10}{100}m = 2 \iff m = 20</math> and <math>\frac{20}{100}j = 2 \iff j = 10</math>, so the desired difference is <math>\left\lvert m-j\right\rvert = 20-10 = \boxed{\ | Let <math>m</math> be Mike's bill and <math>j</math> be Joe's bill (both in dollars). We then have <math>\frac{10}{100}m = 2 \iff m = 20</math> and <math>\frac{20}{100}j = 2 \iff j = 10</math>, so the desired difference is <math>\left\lvert m-j\right\rvert = 20-10 = \boxed{\textbf{(D) } 10}</math>. | ||
==Video Solution 1== | ==Video Solution 1== | ||
Revision as of 15:58, 1 July 2025
Problem
While eating out, Mike and Joe each tipped their server 
. Mike tipped 
of his bill and Joe tipped 
of his bill. What was the difference, in dollars, between their bills?
Solution
Let 
be Mike's bill and 
be Joe's bill (both in dollars). We then have 
and 
, so the desired difference is 
.
Video Solution 1
Video Solution 2
~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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