Question 36·Hard·Linear Equations in One Variable
Pearson Electronics — Zephyr Laptop Clearance
During a one–day clearance event, Pearson Electronics promoted the following price adjustments on the remaining Zephyr laptops:
- 30% off the list price
- An additional $75 off the discounted price at checkout
- An 8% sales tax applied after all discounts
A customer purchased a Zephyr laptop and paid $561.60 in total, including tax. What was the list price, in dollars, of the laptop before any discounts or tax?
For SAT word problems with multiple discounts and tax, introduce a variable for the original price and carefully apply each step in order: convert each percentage to a decimal multiplier (like 30% off → multiply by 0.7, 8% tax → multiply by 1.08), handle fixed dollar changes by adding or subtracting, and then set the resulting expression equal to the given final amount. When solving, reverse the operations one at a time—undo the last percentage or subtraction first—and watch for the common mistake of adding or subtracting percentages instead of multiplying by them.
Hints
Represent the unknown
Let represent the original list price of the laptop before any discounts or tax. Every step in the problem should be written in terms of .
Translate each discount into an expression
After a 30% discount, the customer pays 70% of the list price. How can you write 70% of as a decimal expression? Then, how do you represent taking $75 off that amount?
Account for tax correctly
An 8% tax is not subtracted; it is added as a multiplier. What number do you multiply the pre-tax price by to include an 8% tax? Use that to write an expression for the final total price in terms of .
Set up and solve the equation
Set your expression for the final price (after both discounts and tax) equal to $561.60. Then, undo the operations in reverse order: first undo the tax multiplier, then undo the $75 discount, then undo the 30% discount.
Desmos Guide
Enter the expression for the final price
In Desmos, type the expression y = 1.08*(0.7x - 75) to represent the total amount paid (including tax) as a function of the list price .
Find the list price that gives the known total
Add a second line: y = 561.6 to represent the actual total paid. Look at the point where the graph of y = 1.08*(0.7x - 75) intersects the horizontal line y = 561.6; the x-coordinate of this intersection is the original list price.
Step-by-step Explanation
Define the variable and model the first discount
Let be the list price of the laptop before any discounts or tax.
The laptop is 30% off, so the customer pays 70% of the list price. That means the price after the 30% discount is
Apply the $75 discount
Next, the store takes an additional $75 off the discounted price.
So the price just before tax is
Apply the 8% sales tax
An 8% sales tax means you multiply the pre-tax price by (you pay 100% of the price plus 8% more).
So the total amount the customer pays, including tax, is
We are told this total equals $561.60, so we have the equation
Undo the tax to simplify the equation
To undo the 8% tax, divide both sides of the equation by :
Compute the right-hand side. Since , we get
Solve for the original list price
Now solve the linear equation .
First add to both sides:
Now divide both sides by :
Since ,
So the list price of the laptop before any discounts or tax was $850.