Difference between revisions of "2023 AMC 8 Problems/Problem 18"

(Animated Video Solution)
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~Star League (https://starleague.us)
 
~Star League (https://starleague.us)
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==Written Solution==
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We have <math>2</math> directions going <math>5</math> right or <math>3</math> left. We can assign a variable to each of these directions. We can call going right 1 direction X and we can call going 1 left Y. We can build a equation of <math>5X-3Y=2023</math>. Where we have to limit the number of moves we do. We can do this by making more of our moves the <math>5</math> move turn then the <math>3</math> move turn. The first obvious step is to go some amount of moves in the → direction then subtract off in the ← direction to land on <math>2023</math>. The least amount of <math>3</math>’s added to <math>2023</math> to make a multiple of <math>5</math> is <math>4</math> as <math>2023 + 4(3) = 2035</math>. So now we have solved the problem as we just go <math>\frac{2035}{5} = 407</math> hops right, and just do 4 more hops left. Yielding <math>407 + 4 = \boxed{\text{(D)}411}</math> as our answer.
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~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat

Revision as of 19:56, 24 January 2023

We have $2$ directions going $5$ right or $3$ left. We can assign a variable to each of these directions. We can call going right 1 direction X and we can call going 1 left Y. We can build a equation of $5X-3Y=2023$. Where we have to limit the number of moves we do. We can do this by making more of our moves the $5$ move turn then the $3$ move turn. The first obvious step is to go some amount of moves in the → direction then subtract off in the ← direction to land on $2023$. The least amount of $3$’s added to $2023$ to make a multiple of $5$ is $4$ as $2023 + 4(3) = 2035$. So now we have solved the problem as we just go $\frac{2035}{5} = 407$ hops right, and just do 4 more hops left. Yielding $407 + 4 = \boxed{\text{(D)}411}$ as our answer.


Animated Video Solution

https://youtu.be/zmRiG52jxpg

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

Written Solution

We have $2$ directions going $5$ right or $3$ left. We can assign a variable to each of these directions. We can call going right 1 direction X and we can call going 1 left Y. We can build a equation of $5X-3Y=2023$. Where we have to limit the number of moves we do. We can do this by making more of our moves the $5$ move turn then the $3$ move turn. The first obvious step is to go some amount of moves in the → direction then subtract off in the ← direction to land on $2023$. The least amount of $3$’s added to $2023$ to make a multiple of $5$ is $4$ as $2023 + 4(3) = 2035$. So now we have solved the problem as we just go $\frac{2035}{5} = 407$ hops right, and just do 4 more hops left. Yielding $407 + 4 = \boxed{\text{(D)}411}$ as our answer.


~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat