Difference between revisions of "2023 AMC 10B Problems/Problem 2"
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After the discount, the price becomes <math> 80\%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. | 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{( | + | So, <math>43=86\%x</math>, <math>x=\boxed{\textbf{(B) }\$50}.</math> |
~Mintylemon66 | ~Mintylemon66 | ||
Revision as of 16:24, 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
