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2023 AMC 8 Problems/Problem 11: Difference between revisions

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==Written Solution==
==Solution 1==
Since the answers are so far apart, we just need to compute the # of figures the answer contains. So by approximating all the values for the hourly rate we have <math>\frac{300,000,000}{5 * 30 * 30} \approx \frac{300,000,000}{5000} = 60,000</math> which is <math>\boxed{\text{(C)}60,000}</math>  
Since the answers are so far apart, we just need to compute the # of figures the answer contains. So by approximating all the values for the hourly rate we have <math>\frac{300,000,000}{5 * 30 * 30} \approx \frac{300,000,000}{5000} = 60,000</math> which is <math>\boxed{\text{(C)}60,000}</math>  


~apex304
~apex304
==Solution 2==
<math>292,526,838</math> miles is extremely close to <math>300,000,000</math> miles. We also know that <math>6.5</math> months is equivalent to <math>6.5\cdot30\cdot24</math> hours. Now, we can calculate the speed in miles per hour, which we find is about <math>\boxed{\textbf{(C) }60,000}</math>.
<cmath>\dfrac{300000000}{6.5\cdot30\cdot24}=\dfrac{10000000}{6.5\cdot24}\\
=\dfrac{10000000}{13\cdot12}\\
=\dfrac{10000000}{156}\\
\approx\dfrac{10000000}{150}\\
\approx\dfrac{200000}{3}\\
\approx60000</cmath>
~MathFun1000


==Animated Video Solution==
==Animated Video Solution==

Revision as of 22:04, 24 January 2023

Solution 1

Since the answers are so far apart, we just need to compute the # of figures the answer contains. So by approximating all the values for the hourly rate we have $\frac{300,000,000}{5 * 30 * 30} \approx \frac{300,000,000}{5000} = 60,000$ which is $\boxed{\text{(C)}60,000}$

~apex304

Solution 2

$292,526,838$ miles is extremely close to $300,000,000$ miles. We also know that $6.5$ months is equivalent to $6.5\cdot30\cdot24$ hours. Now, we can calculate the speed in miles per hour, which we find is about $\boxed{\textbf{(C) }60,000}$.

\[\dfrac{300000000}{6.5\cdot30\cdot24}=\dfrac{10000000}{6.5\cdot24}\\ =\dfrac{10000000}{13\cdot12}\\ =\dfrac{10000000}{156}\\ \approx\dfrac{10000000}{150}\\ \approx\dfrac{200000}{3}\\ \approx60000\]

~MathFun1000

Animated Video Solution

https://youtu.be/hwR2VM9tHJ0

~Star League (https://starleague.us)

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