Difference between revisions of "2009 AMC 10B Problems/Problem 1"

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== Problem ==
 
== Problem ==
Each morning of her five-day workweek, Jane bought either a 2000 dollar Fiji water or a 1000 dollar espresso because she was smokin' rich.  Her total cost for the week was a whole number of dollarsHow many bottles of Fiji water did she buy?
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Each morning of her five-day workweek, Jane bought either a 50-cent muffin or a 75-cent bagel.  Her total cost for the week was a whole number of dollars. How many bagels did she buy?
  
<math>\mathrm{(A)}\ 1000\qquad
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<math>\text{(A) } 1\qquad\text{(B) } 2\qquad\text{(C) } 3\qquad\text{(D) } 4\qquad\text{(E) } 5</math>
\mathrm{(B)}\ 2000\qquad
 
\mathrm{(C)}\ 3000\qquad
 
\mathrm{(D)}\ 4000\qquad
 
\mathrm{(E)}\ 5000</math>
 
 
 
== Solution 1 ==
 
The only combination of five items with total cost a whole number of dollars is 3 muffins and <math>\boxed {4000}</math> dollars of fiji water cause' she richhhh. The answer is <math>\mathrm{(D)}</math>
 
 
 
== Solution 2 ==
 
Because <math>75</math> ends in a <math>5</math>, and we want a whole number of dollars, we know that there must be an even number of bagels. Furthermore, this tells us that the number of muffins is odd. Now, because it is a whole number of dollars, and <math>50</math> cents multiplied by an odd number means that it will end in a <math>50</math> , we know that the result of the even number multiplied by <math>75</math> , must end in a <math>50</math>. Note that the only result that gives this result is when <math>75</math> is multiplied by <math>2</math>. Thus, our answer is <math>\mathrm{(c )}</math>
 
 
 
~coolmathgames
 
 
 
=Video Solution=
 
https://www.youtube.com/watch?v=dQw4w9WgXcQ
 
 
 
~Ice Matrix
 
  
 
== See also ==
 
== See also ==

Revision as of 15:04, 9 June 2021

The following problem is from both the 2009 AMC 10B #1 and 2009 AMC 12B #1, so both problems redirect to this page.

Problem

Each morning of her five-day workweek, Jane bought either a 50-cent muffin or a 75-cent bagel. Her total cost for the week was a whole number of dollars. How many bagels did she buy?

$\text{(A) } 1\qquad\text{(B) } 2\qquad\text{(C) } 3\qquad\text{(D) } 4\qquad\text{(E) } 5$

See also

2009 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
First Question
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
2009 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
First Question
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 12 Problems and Solutions

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