Price Tag Postmortem Handout Final
Price Tag Postmortem
Deconstructing Common Percent Discount Errors
Name:
Date:
1
Case Study: The Grocery Bill
"Sally has a discount card that reduces the price of her grocery bill by 5%. If \(c\) represents the cost of Sally’s groceries, which expression represents Sally’s grocery bill?"
The Solution: Option B (\(0.95c\))
When you save 5%, you are still paying for 95% of the total cost. Since "percent" means "per hundred," 95% is \(0.95\). We multiply this by the original cost (\(c\)) to find the final bill in one easy step.
Why the others were wrong
A
\(0.05c\)
This finds the savings amount (how much you get off), not the price paid. If the bill was $100, this says the total is only $5. That's a massive discount, but mathematically incorrect for the final bill!
C
\(c - 0.05\)
This is a Units Error. It subtracts 5 cents (\(0.05\)) from the total. A 5% discount is proportional to the price; it isn't just a nickel off every bill.
2
Case Study: The Sale Hat
"A hat has a regular price of \(x\) dollars. During a sale, it is discounted by 20%. The expression \(0.8x\) describes the price. Which expression also describes the price?"
The Solution: Option D (\(x - 0.2x\))
This expression shows the two parts of the transaction: the Original Price (\(x\)) minus the Discount Amount (\(0.2x\)). Subtracting 20% of the price from the full price gives you the same 80% total that \(0.8x\) represents.
Spot the Trap
A
0.2x is just the savings. It leaves out the price!
B
x - 20 subtracts 20 dollars, not 20%.
C
x - 0.2 subtracts 20 cents, not 20%.
The Golden Rule of Percents
In algebra, a percentage cannot stand alone in an expression. It must always be attached to its base. Never add or subtract a raw decimal like 0.05—you must multiply it by the variable first!
