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Difference between revisions of "2023 AMC 10B Problems/Problem 2"

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~Mintylemon66
 
~Mintylemon66
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==Solution==
 
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Original price = <math>\dfrac{43}{0.8 \cdot 1.075} = 50.</math>
 
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That's ugly.  We can sort of see that <math>\$43</math> is slightly greater than <math>\$40</math> which is 80% of <math>\$50</math>.
 
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So <math>50\cdot0.8\cdot1.1=44</math> which is slightly greater than <math>\$43</math>, confirming <math>\boxed{\textbf{(E) }\$50}.</math>
 
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~Technodoggo
 

Revision as of 14:55, 15 November 2023

Problem

Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\%$on every pair of shoes. Carlos also knew that he had to pay a $7.5\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy?


$\textbf{(A) }$46\qquad\textbf{(B) }$47\qquad\textbf{(C) }$48\qquad\textbf{(D) }$49\qquad\textbf{(E) }$50$

Solution

Let the original price be $x$ dollars. After the discount, the price becomes $80\%x$ dollars. After tax, the price becomes $80\% \times (1+7.5\%) = 86\% x$ dollars. So, $43=86\%x$, $x=\boxed{\textbf{(E) }$50}.$

~Mintylemon66

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