Difference between revisions of "2023 AMC 12B Problems/Problem 2"
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<math>\textbf{(A) }$46\qquad\textbf{(B) }$50\qquad\textbf{(C) }$48\qquad\textbf{(D) }$47\qquad\textbf{(E) }$49 </math> | <math>\textbf{(A) }$46\qquad\textbf{(B) }$50\qquad\textbf{(C) }$48\qquad\textbf{(D) }$47\qquad\textbf{(E) }$49 </math> | ||
+ | |||
+ | ==Solution 1== | ||
+ | We can create the equation: | ||
+ | <cmath>0.8x \cdot 1.075 = 43</cmath> | ||
+ | using the information given. This is because x, the original price, got reduced by 20%, or multiplied by 0.8, and it also got multiplied by 1.075 on the discounted price. Solving that equation, we get | ||
+ | <cmath>\frac{4}{5} \cdot x \cdot \frac{43}{40} = 43</cmath> | ||
+ | <cmath>\frac{4}{5} \cdot x \cdot \frac{1}{40} = 1</cmath> | ||
+ | <cmath>\frac{1}{5} \cdot x \cdot \frac{1}{10} = 1</cmath> | ||
+ | <cmath>x = \boxed{50}</cmath> | ||
+ | |||
+ | ~lprado |
Revision as of 17:40, 15 November 2023
Problem
Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by on every pair of shoes. Carlos also knew that he had to pay a sales tax on the discounted price. He had dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy?
Solution 1
We can create the equation: using the information given. This is because x, the original price, got reduced by 20%, or multiplied by 0.8, and it also got multiplied by 1.075 on the discounted price. Solving that equation, we get
~lprado