Question 175·200 Super-Hard SAT Math Questions·Algebra
To refinish a wooden deck, a person applies 1 coat of primer and then 2 coats of sealant.
- One gallon of primer costs $24 and covers 60 square feet.
- One gallon of sealant costs $35 and covers 75 square feet.
Only 85% of the deck’s area needs primer, and only 95% of the deck’s area needs sealant.
Because of spills, the person plans to buy 8% more sealant than the exact amount needed, but no extra primer. The deck has area square feet.
Which equation represents the total cost , in dollars, of primer and sealant needed?
Convert each real-world modifier into a multiplier on the area first (e.g., , ), then handle coats and “extra” as additional multipliers on gallons. After that, convert gallons to dollars and add the resulting linear expressions to get in the form .
Hints
Use area fractions first
Replace “85% of ” with (or ) and “95% of ” with (or ) before dividing by coverage.
Apply coats and extra sealant in the right places
Two coats multiplies the sealant gallons by 2. The 8% extra multiplies only the sealant amount by .
Turn each product into a cost-per- expression
Compute primer cost as (cost per gallon)(gallons needed) and do the same for sealant, then add the two coefficients of .
Desmos Guide
Enter the total cost function
Type:
T(d)=24*(0.85*d/60)+35*1.08*(2*(0.95*d)/75)
Evaluate at a convenient value of d
Set (or another convenient value).
In Desmos, either create a slider for d and set it to 500 or evaluate T(500).
Check which answer choice matches
For each answer choice, substitute and evaluate.
The only expression that matches T(500) is the correct equation.
Step-by-step Explanation
Write gallons needed (including area percentages and coats)
Primer is used on only of the deck:
Primer gallons .
Sealant is used on only of the deck, and there are 2 coats:
Exact sealant gallons .
Account for the extra sealant
Buying 8% extra sealant means multiplying the exact sealant gallons by :
Sealant gallons to buy .
Primer gallons stay .
Convert gallons to cost
Primer cost:
Sealant cost:
Add the costs
Add the coefficients:
Therefore, the equation is .