If, after receiving a 20% discount when buying a television set, and after paying 7% tax, you paid $642, what was the original marked price of the TV set?

To find the television's original sticker price, you have to work backward and reverse each transaction, starting from the final amount paid. The $642 total includes the 7% sales tax. This means the final price represents 107% of the discounted price. A common mistake is to simply subtract 7% from the total. Instead, to find the pre-tax amount, you must divide $642 by 1.07. This calculation reveals that the price after the discount, but before tax, was exactly $600.

With the $600 discounted price figured out, the next step is to reverse the 20% discount. This $600 sale price represents the remaining 80% of the original cost (100% minus the 20% that was taken off). To find the full, 100% original price, you divide the discounted price of $600 by 0.80. This gives you the original marked price of the television set.

This type of "reverse percentage" problem is a practical skill for smart shoppers. It demonstrates how discounts are almost always calculated on the pre-tax price, and it highlights the key mathematical rule for undoing percentages: you must divide by the percentage (as a decimal), not simply subtract it. By unwrapping the final cost one layer at a time, you can always work your way back to the starting point.