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| − | ==Problem==
| + | #redirect[[2023 AMC 12A Problems/Problem 2]] |
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| − | 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?
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| − | <math>\textbf{(A) }\$47\qquad\textbf{(B) }\$50\qquad\textbf{(C) }\$46\qquad\textbf{(D) }\$48\qquad\textbf{(E) }\$49 </math>
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| − | ==Solution 1==
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| − | Let the original price be <math>x</math> dollars.
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| − | After the discount, the price becomes <math> 80\%x</math> dollars.
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| − | After tax, the price becomes <math> 80\% \times (1+7.5\%) = 86\% x </math> dollars.
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| − | So, <math>43=86\%x</math>, <math>x=\boxed{\textbf{(B) }\$50}.</math>
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| − | ~Mintylemon66
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| − | ~ Minor tweak:Multpi12
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| − | ==Solution 2==
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| − | 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{(B) }\$50}</math>.
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| − | ~vsinghminhas
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| − | ==Solution 3 (Intuition and Guessing)==
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| − | We know the discount price will be 5/4, and 0.075 is equal to 3/40. So we look at answer choice <math>\textbf{(B) }</math>, see that the discoutn price will be 40, and with sales tax applied it will be 43, so the answer choice is <math>\boxed{\textbf{(B) }\$50}</math>.
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| − | ~lucaswujc
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