One gallon of sealant costs 13 and will cover 300 square feet of a surface. A deck has a total surface area of d square feet. Which equation represents the cost c, in dollars, of the sealant needed to cover the deck twice?

One gallon of sealant costs 13 and will cover 300 square feet of a surface. A deck has a... | SAT Ratios, rates, proportional relationships, and units Practice

Answer: C. $c = 13(\dfrac{d}{150})$

Explanation:

$1$ . Determine the total area to be covered:

- The deck has a surface area of d square feet.

- It needs to be covered twice.

- Total Area = $2 \times d = 2d$ square feet.

$2$ . Calculate the number of gallons needed:

- Each gallon covers $300$ square feet.

- Gallons Needed = $\dfrac{\text{Total Area}}{\text{Coverage per Gallon}} = \dfrac{2d}{300}$

- Simplify this fraction: Gallons Needed = $\dfrac{d}{150}$ .

$3$ . Calculate the total cost (c):

- The cost is the number of gallons needed multiplied by the price per gallon.

- Price per gallon is $ $13$ .

- Total Cost $c$ = (Gallons Needed) $\times$ (Price per Gallon)

- $c = (\dfrac{d}{150}) \times 13$

$4$ . Rewrite the equation and compare with options:

- The equation can be written as $c = 13(\dfrac{d}{150})$ .

- This matches option C.

$5$ . Conclusion:

- The correct equation for the total cost is C.