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A store has a 40% off sale on headphones. With this discount, the price of one pair of headphones is $36. What is the original price of the pair of headphones? $ ◻

A store has a 40%40\% off sale on headphones. With this discount, the price of one pair of headphones is $36\$36.\newline What is the original price of the pair of headphones?\newline $□\$\square

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Full solution

Q. A store has a 40%40\% off sale on headphones. With this discount, the price of one pair of headphones is $36\$36.\newline What is the original price of the pair of headphones?\newline $□\$\square
  1. Identify Sale Price: We know the sale price of the headphones is $36\$36 after a 40%40\% discount. To find the original price, we need to determine what price would result in $36\$36 after a 40%40\% reduction.
  2. Denote Original Price: Let's denote the original price as PP. A 40%40\% discount means the customer pays 60%60\% of the original price (100%−40%=60%100\% - 40\% = 60\%). Therefore, 60%60\% of PP is equal to $36\$36.
  3. Set Up Equation: We can set up the equation: 0.60×P=$(36)0.60 \times P = \$(36). To find PP, we divide both sides of the equation by 0.600.60.
  4. Solve for Original Price: P=$(36)0.60P = \frac{\$(36)}{0.60}P=$(60)P = \$(60)
  5. Final Result: The original price of the headphones was $60\$60 before the 40%40\% discount.

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