A laptop that normally sells for $600 is placed on sale. First, its price is reduced by . Then an additional discount is applied to the new sale price, resulting in a final price of $408.
What is the value of ?
Back-to-back discounts are successive percent changes: each cut is taken from the price immediately before it. Turn each discount into a multiplier for the fraction left, then multiply both factors by the original price and set the result equal to the final price. Use a one-variable Desmos regression to find the missing percent. Adding the rates fails because the second discount has a different base.
Hints
- Hint 1
A discount multiplier is the fraction of a price that remains after a cut. If the first cut removes of the original price, what fraction of the original $600 remains?
- Hint 2
The base of a percent is the amount it is taken from. The additional is taken from the new sale price, not from $600. What fraction of that new price remains?
Step-by-step
Multiply the discounts, then solve in Desmos
Step 1Write the price after the first discount
The first discount removes , or , of the original $600. So the fraction left is , and the new price is:
- Step 2
Find the fraction left after the second discount
The second discount is taken from the reduced price, not from the original price. Subtract its from the whole price to find its multiplier, the fraction kept:
- Step 3
Set the final price equal to the result
Multiply the first sale price by because that is the fraction left after the second cut. The problem says the result is $408, so:
- Step 4
Solve for the first discount
Type in Desmos. Use instead of so Desmos solves for the unknown rather than graphing it; tells it to fit the equation. Under PARAMETERS, Desmos shows . So the first discount was . Choice B.