A backpack originally costs $50. During a sale, its price is reduced by 20%. What is the sale price of the backpack?
A sale discount is a percent decrease from the original price. The cue is “reduced by”: start with 100% of the original and subtract the discount percent. Then use Desmos to find the percent left of the original price. Calculating only the discount gives the amount saved, not what you pay.
Hints
- Hint 1
The original price is 100% of itself. A discount takes away part of that full price. If 20% is removed, what percent of the original price is left to pay?
- Hint 2
A base is the amount a percent is taken of. Here, that’s the original price, not the discount. Once you know the percent left, take that percent of the original $50.
Step-by-step
Find the percent left to pay
Step 1Find the percent remaining
A discount removes part of the full price, which is 100% of itself. Taking off 20% leaves:
Use the percent left, not the percent removed, to find what you pay.
- Step 2
Apply that percent to the original price
The original $50 is the base, the amount the percent is taken of. Let be the sale price, so:
Using here would find only the discount.
- Step 3
Calculate the sale price
Type in Desmos. It shows , so the backpack’s sale price is $40. Choice C.