\( 1 \leftarrow \) After a \( 65 \% \) reduction, you purchase a new sofa on sale for \( \$ 175 \). What was the original price of the sofa?

To find the original price of the sofa, you can start by letting \( x \) represent the original price. Since there was a \( 65\% \) reduction, you are paying \( 35\% \) of the original price. Thus, you can set up the equation: \[ 0.35x = 175 \] To solve for \( x \), divide both sides by \( 0.35 \): \[ x = \frac{175}{0.35} \] Calculating that gives: \[ x = 500 \] So, the original price of the sofa was \( \$500 \). If you ever find yourself scratching your head over percentages, remember this nifty trick: to find what percentage of a number you're left with after a reduction, just subtract the percentage of the reduction from 100%. It’s like a tiny math cheat sheet that keeps everything in check! For those who love exploring, check out some classic consumer psychology books that delve into how pricing strategies, like discounts, affect our buying decisions. "Predictably Irrational" by Dan Ariely is a fantastic read that dives into the quirky ways our minds affect our spending habits!📚✨