2023 AMC 10B Problems/Problem 2
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
~ Minor tweak:Multpi12
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
Solution 3 (Intuition and Guessing)
We know the discount price will be 5/4, and 0.075 is equal to 3/40. So we look at answer choice , see that the discoutn price will be 40, and with sales tax applied it will be 43, so the answer choice is
.
~lucaswujc