A unit rate turns each material’s price and coverage into dollars per square foot. For a layered cost question, calculate each material’s cost for one square foot of deck in Desmos, then add the rates and multiply by the deck’s area. Keep track of which material each percent describes: an allowance for extra sealant must not raise the primer cost.
Hints
- Hint 1
A unit rate gives the cost for one square foot. Divide the primer’s price by the area one gallon covers, then apply that rate to the portion of the deck that needs primer.
- Hint 2
The same part of the deck gets two sealant coats. Each coat uses sealant, so double the coverage needed for one coat before working out the sealant cost.
- Hint 3
Buying 8% more sealant means buying 108% of the exact sealant amount. Apply that increase after accounting for both coats, but don’t apply it to primer.
Step-by-step
Build the cost per square foot
Step 1Find the primer cost per square foot of deck
Primer costs $24 for 60 square feet of coverage, so its unit rate is dollars per square foot covered. Only of the deck needs it. Type in Desmos; it shows . So primer costs dollars for a deck of square feet.
- Step 2
Account for both sealant coats
One sealant coat costs dollars per square foot covered. The two coats cover the same of the deck twice, so type . Desmos shows dollars per square foot of deck for the exact sealant needed. Keep that value unrounded.
- Step 3
Add the extra sealant
Buying more than the exact sealant amount means buying of it. Type ; Desmos shows dollars per square foot of deck. Apply each percent only to the material it describes. The extra is sealant, so the primer rate stays unchanged.
- Step 4
Write the total cost equation
Add the two dollar-per-square-foot rates. Type ; Desmos shows . Use its fraction button to read . Multiplying that rate by the deck’s square feet gives the total cost, dollars. Choice C.