Difference between revisions of "2023 AMC 10B Problems/Problem 2"
Technodoggo (talk | contribs) (→Solution) |
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<math>\textbf{(A) }\$46\qquad\textbf{(B) }\$47\qquad\textbf{(C) }\$48\qquad\textbf{(D) }\$49\qquad\textbf{(E) }\$50 </math> | <math>\textbf{(A) }\$46\qquad\textbf{(B) }\$47\qquad\textbf{(C) }\$48\qquad\textbf{(D) }\$49\qquad\textbf{(E) }\$50 </math> | ||
| − | ==Solution== | + | ==Solution 1== |
Let the original price be <math>x</math> dollars. | Let the original price be <math>x</math> dollars. | ||
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~Mintylemon66 | ~Mintylemon66 | ||
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| + | ==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>c=\boxed{\textbf{(E) }\$50}</math>. | ||
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| + | ~vsinghminhas | ||
Revision as of 15:03, 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
Let the original price be 
dollars.
After the discount, the price becomes 
dollars.
After tax, the price becomes 
dollars.
So, 
, 
~Mintylemon66
Solution 2
We can assign a variable 
to represent the original cost of the running shoes. Next we set up the equation 
. We can solve this equation for and get 
.
~vsinghminhas
