A successive percent increase is signaled when one charge is calculated on a price that already includes another charge. Turn each charge into a multiplier, then use a Desmos regression to work backward from the total to the original price. Apply each percent to the amount named as its base. Adding the percentages would treat them as if they had the same base.
Hints
- Hint 1
A premium is an added charge. The bid is of itself, so adding a premium makes the price before tax of the bid. If the bid is , what is that price?
- Hint 2
The base of a percent is the amount it’s taken from. The tax base includes the premium, not only the winning bid. Multiply the price before tax by , then connect that result to the total paid.
Step-by-step
Work backward from the total
Step 1Add the premium to the bid
Let be the winning bid in dollars. The premium adds of , so keep the whole bid and add that charge:
- Step 2
Apply tax to the updated price
The tax is of the bid plus premium, which is . Adding tax makes the total , or times, that price:
Don't add and : the base for the tax is larger than the original bid.
- Step 3
Match the expression to the amount paid
The expression includes the bid and both charges, so set it equal to the given total:
- Step 4
Find the winning bid in Desmos
For a regression, replace with and with . Type ; Desmos finds the value that makes the two sides match. Under PARAMETERS, it shows . That's the winning bid in dollars, so $952 is closest. Choice B.