Final answer:
To paint the room, Henry will need 4 gallons of paint, costing a total of $72.
Step-by-step explanation:
To find the cost of painting the room, we first need to calculate the total area of all four walls. Each wall is 12 feet by 14 feet, so the area of one wall is 12 * 14 = 168 square feet. Since there are four walls, the total area of all four walls is 168 * 4 = 672 square feet.
Since two coats of paint are required, we need to double the total area, so the total area to be painted is 672 * 2 = 1344 square feet.
Next, we need to determine how many gallons of paint we will need. Each gallon covers 350 square feet, so the number of gallons needed is 1344 / 350 = 3.84 gallons. Since we can't buy a fraction of a gallon, we will need to round up to the nearest whole gallon, so Henry will need to buy 4 gallons of paint.
Finally, to calculate the cost, we multiply the number of gallons by the cost of one gallon. Henry will need 4 gallons of paint, and each gallon costs $18, so the total cost will be 4 * $18 = $72.