Difference between revisions of "2023 AMC 10B Problems/Problem 2"
Mintylemon66 (talk | contribs) |
Technodoggo (talk | contribs) (→Solution) |
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So, <math>43=86\%x</math>, <math>x=\boxed{\textbf{(E) }$50}.</math> | 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 |
Revision as of 15:54, 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
Let the original price be 
dollars.
After the discount, the price becomes 
dollars.
After tax, the price becomes 
dollars.
So, 
, 
~Mintylemon66
Solution
Original price = 
That's ugly. We can sort of see that is slightly greater than 
which is 80% of 
.
So 
which is slightly greater than , confirming 
~Technodoggo
