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Difference between revisions of "2001 AMC 8 Problems/Problem 10"

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==Problem==
 
==Problem==
  
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Bob Bluster, the KNEWS meteorologist, determined that the mathematical odds of <math>\emph{no rain}</math> tomorrow are 11:9. What would a mathematics student determine as the percent chance there <math>\emph{will be rain}</math> tomorrow?
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A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?
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<math>\text{(A)}\ 20\text{ dollars} \qquad \text{(B)}\ 50\text{ dollars} \qquad \text{(C)}\ 200\text{ dollars} \qquad \text{(D)}\ 500\text{ dollars} \qquad \text{(E)}\ 2000\text{ dollars}</math>
  
 
==Solution==
 
==Solution==
  
 
<math> 2000\% </math> is equivalent to <math> 20\times100\% </math>. Therefore, <math> 2000\% </math> of a number is the same as <math> 20 </math> times that number. <math> 4 </math> quarters is <math> 1 </math> dollar, so Bryden will get <math> 20\times1={20} </math> dollars, <math> \boxed{\text{A}} </math>.
 
<math> 2000\% </math> is equivalent to <math> 20\times100\% </math>. Therefore, <math> 2000\% </math> of a number is the same as <math> 20 </math> times that number. <math> 4 </math> quarters is <math> 1 </math> dollar, so Bryden will get <math> 20\times1={20} </math> dollars, <math> \boxed{\text{A}} </math>.
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==Solution 2==
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Since <math> 2000\% </math> is just <math>\frac{2000}{100}</math>, we can multiply that by <math>100</math>, because four quarters is a <math>100</math> cents. After the multiplication, we get <math>2000</math>. Since our answer is in cents right now, we need to convert it to dollars, which would be <math>\boxed{\text{(A) 20}}</math> dollars.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2001|num-b=9|num-a=11}}
 
{{AMC8 box|year=2001|num-b=9|num-a=11}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 21:41, 10 January 2023

Problem

A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?

$\text{(A)}\ 20\text{ dollars} \qquad \text{(B)}\ 50\text{ dollars} \qquad \text{(C)}\ 200\text{ dollars} \qquad \text{(D)}\ 500\text{ dollars} \qquad \text{(E)}\ 2000\text{ dollars}$

Solution

$2000\%$ is equivalent to $20\times100\%$. Therefore, $2000\%$ of a number is the same as $20$ times that number. $4$ quarters is $1$ dollar, so Bryden will get $20\times1={20}$ dollars, $\boxed{\text{A}}$.

Solution 2

Since $2000\%$ is just $\frac{2000}{100}$, we can multiply that by $100$, because four quarters is a $100$ cents. After the multiplication, we get $2000$. Since our answer is in cents right now, we need to convert it to dollars, which would be $\boxed{\text{(A) 20}}$ dollars.

See Also

2001 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 9 		Followed by
Problem 11
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 AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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