A successive percent change happens when a price changes and then changes again. Turn each increase or discount into a multiplier, then multiply the factors in Desmos to compare the final price with the original. The later percent uses the price left by the earlier change. Subtracting the stated percents directly treats them as though they share the same base.
Hints
- Hint 1
An increase adds to the whole original price. Since the whole price is , what multiplier represents keeping it and adding the ?
- Hint 2
A discount removes part of its current base. The comes off the price after the increase. What fraction of that higher price is left?
- Hint 3
A net percent change compares the final price with the starting price. Multiply the two factors, then compare their product with , which represents all of the original price.
Step-by-step
Multiply the price-change factors
Step 1Find the increase factor
The increase keeps the whole original price and adds of it. Find its multiplier, the number that scales the price:
- Step 2
Find the discount factor
The discount uses the new, higher price as its base, the amount the percent is taken of. It leaves the whole higher price minus of it. Subtract to find its multiplier:
- Step 3
Find the final fraction of the original price
Type in Desmos. It returns , so of the original price remains. Multiply the factors because the discount applies to the increased price; the overall multiplier takes you from the original price straight to the final price.
- Step 4
Find the change from the original
The question asks for the change, not the percent of the price that remains. Subtract from the original to find the percent decrease: . The laptop’s price is lower than its original regular price. Choice D.