Question 10·Easy·Percentages
A backpack originally costs $50. During a sale, its price is reduced by 20%. What is the sale price of the backpack?
For percent decrease problems, first decide if it’s easier to find the discount or the remaining percent of the original. Convert the percent to a decimal, then either (1) multiply the original amount by the discount percent and subtract from the original, or (2) subtract the percent from 100% and multiply the original amount by that remaining percent. Always check whether your final answer makes sense—after a discount, the new price should be less than the original.
Hints
Identify the operation
The phrase "reduced by 20%" means the price goes down. Should you be adding or subtracting from the original $50?
Work with the percentage
Turn into a decimal. What number should you multiply by to find of it?
Choose your preferred method
You can either find of and subtract that from , or directly find of (because that's the portion you still pay).
Finish the calculation
After you find the discount amount or the remaining percentage, do the final multiplication or subtraction carefully to avoid a simple arithmetic mistake.
Desmos Guide
Use Desmos to compute the sale price
In Desmos, type either 50*(1-0.20) or 50*0.80 and look at the output. The value Desmos gives is the sale price after a 20% discount is applied to $50.
Step-by-step Explanation
Understand what a 20% discount means
A 20% discount means the price is lowered by 20% of the original price. So you either:
- Find 20% of and subtract that from , or
- Pay the remaining of the original price.
Convert the percent to a decimal
Convert and to decimals:
- You can use either one depending on which method you choose.
Find the discount amount (optional method)
If you choose the "subtract the discount" method:
- Calculate of :
This tells you the discount is $10, which you will subtract from the original price.
Compute the final sale price
Now subtract the discount from the original price:
- Original price: $50
- Discount: $10
- Sale price: $50 - $10 = $40
So, the sale price of the backpack is $40.