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

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==Problem==
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#redirect[[2023 AMC 12B Problems/Problem 2]]
 
 
Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by <math>20\% </math>on every pair of shoes. Carlos also knew that he had to pay a <math>7.5\%</math> sales tax on the discounted price. He had <math> \$43 </math> dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy?
 
 
 
 
 
<math>\textbf{(A) }\$47\qquad\textbf{(B) }\$50\qquad\textbf{(C) }\$46\qquad\textbf{(D) }\$48\qquad\textbf{(E) }\$49 </math>
 
 
 
==Solution 1==
 
 
 
Let the original price be <math>x</math> dollars.
 
After the discount, the price becomes <math> 80\%x</math> dollars.
 
After tax, the price becomes <math> 80\% \times (1+7.5\%) = 86\% x </math> dollars.
 
So, <math>43=86\%x</math>, <math>x=\boxed{\textbf{(B) }\$50}.</math>
 
 
 
~Mintylemon66
 
 
 
==Solution 2==
 
We can assign a variable <math>c</math> to represent the original cost of the running shoes. Next, we set up the equation <math>80\%\cdot107.5\%\cdot c=43</math>. We can solve this equation for <math>c</math> and get <math>\boxed{\textbf{(E) }\$50}</math>.
 
 
 
~vsinghminhas
 

Latest revision as of 19:53, 15 November 2023