Percent Discounts: The Sale Tag Is Doing Math at You
You spot a jacket marked 25% off. Your brain announces, “Basically free.” Your bank account would like to submit a correction. Percent discounts are useful precisely when a colorful sign is trying to rush the conversation.
Start here
Percent means out of 100. A 25% discount removes one quarter of the original price. It does not mean subtract $25 unless the starting price happens to be $100. The starting amount is the part people forget when the sale rack starts flirting.
Walk through it
For an $80 jacket, convert 25% to 0.25. Multiply: 80 × 0.25 = 20. That is the discount, not the checkout price. Subtract: 80 − 20 = $60 before any tax or other charges. Quick check: a discounted price should be lower than the original.
The faster route
You keep 75% of the price after removing 25%. Calculate 80 × 0.75 = $60. Both methods work; choose the one that makes sense to you.
Level up: two discounts
Suppose the store takes another 10% off the reduced $60 price. That saves $6, leaving $54. It is not a 35% discount on $80: the second percentage uses a smaller starting amount. The total savings are $26, or 32.5% of $80.
Try it
A $40 backpack is 20% off. What is the sale price? If another 10% comes off that sale price, what do you pay before tax?
Check your answer
First: 40 × 0.80 = $32. Next: 32 × 0.90 = $28.80. The second discount saves $3.20. It does not save another $4.
Save this
Discount = original price × decimal rate. Sale price = original price × (1 − decimal rate). For stacked discounts, update the price after each step. The receipt is a word problem with a return policy.
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