|
(Tag: Redirect target changed) |
| (15 intermediate revisions by 6 users not shown) |
| Line 1: |
Line 1: |
| − | ==Problem==
| + | #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) }\$46\qquad\textbf{(B) }\$47\qquad\textbf{(C) }\$48\qquad\textbf{(D) }\$49\qquad\textbf{(E) }\$50 </math>
| |
| − |
| |
| − | ==Solution==
| |
| − | | |
| − | 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{(E) }\$50}.</math>
| |
| − | | |
| − | ~Mintylemon66
| |
| − | | |
| − | ==Solution==
| |
| − | Original price = <math>\dfrac{43}{0.8 \cdot 1.075} = 50.</math>
| |
| − | 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>.
| |
| − | So <math>50\cdot0.8\cdot1.1=44</math> which is slightly greater than <math>\$43</math>, confirming <math>\boxed{\textbf{(E) }\$50}.</math>
| |
| − | | |
| − | ~Technodoggo
| |
