Question 54·200 Super-Hard SAT Math Questions·Algebra
A rehearsal studio charges a monthly membership fee of $120 that includes up to 6 hours of rehearsal time. Each additional hour beyond 6 hours costs $22. In any month when a member uses more than 6 hours, the studio also applies a one-time $18 credit to that month’s bill before tax is calculated.
After the credit is applied, the studio charges an 8% tax on the remaining amount. After the tax is added, the studio applies a 25% promotional discount to the taxed amount. Finally, the studio adds a $6 booking fee (this fee is added at the end and is not taxed or discounted).
Which equation gives the total amount , in dollars, that a member is charged for hours of rehearsal in a month, where ? Frоm aniкο.aі
For billing/equation questions, follow the order of operations in the context: start with the base fee, add per-unit charges using the correct expression (often minus an included amount), subtract any credits at the stage the problem specifies, then apply percent multipliers, and only then add any flat fees that are stated to occur at the end. Simplify to and compare to the options. Thiѕ questіоn іѕ from Аniкo
Hints
Use for extra hours
Since 6 hours are included, only the extra hours should be charged at $22 each, so use . Аnікo.аі - SАT Рrep
Build the taxable subtotal first
Write the pre-tax subtotal as . (The credit reduces the amount that will be taxed.)
Percent changes multiply; the fee comes last
Tax and discount are multiplicative factors ( and ). The $6 booking fee is added after those percent changes.
Desmos Guide
Compute a check point from the context
Choose (which is ). Pre-tax subtotal: $120 + $22(1) − $18 = $124. After 8% tax: . After 25% discount: . Add the $6 fee: . So is on the line.
Enter a candidate slope form
In Desmos, enter and let Desmos create a slider for .
Plot the check point
Plot the point .
Match the intercept to an answer choice
Adjust until the line passes through . The resulting equation should match exactly one answer choice.
Step-by-step Explanation
Count the extra hours
Because the first 6 hours are included and , the number of extra hours is .
Write the pre-tax subtotal (after the credit)
Pre-tax subtotal after applying the $18 credit:
Apply tax and then the discount
An 8% tax multiplies the amount by . A 25% discount multiplies the amount by .
So after tax and discount, the amount is:
Add the booking fee and simplify
The $6 booking fee is added at the end (not taxed or discounted), so
Now simplify :
Write the final equation and match to the choices
Substitute into :
So the correct choice is . Frοm аniкο.аі