Help how to solve this

I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?

Guest Aug 1, 2023

#1**0 **

According to the given information, the wall is 12 meters tall and 120 meters long. This means that the total area of the wall is \(12\text{m} * 120\text{m} = 1440\text{m}^2\).

Also, a gallon of paint covers \(150\text{ft}^2\). Notice how \(\text{ft}^2\) and \(\text{m}^2\) are different units, so we have to perform a conversion so that we can compare these units. Luckily, the problem provides the conversion factor, namely \(1 \text{ft} = 0.3048\text{m}\).

\(150\text{ft}^2 * \frac{0.3048^2 \text{m}^2}{1^2 \text{ft}^2} \approx 13.9355\text{m}^2\). In other words, a gallon of paints covers \(13.9355\text{m}^2\) of area.

Now, \(\frac{1440\text{m}^2}{13.9355\text{m}^2} \approx 103.3335 \text{gallons}\) of paint. However, this is not the final answer because you can only purchase whole gallons of paint. You could purchase 103 gallons of paint, but you would require 0.3335 more gallons of paint to complete the job. Therefore, you would be forced to purchase 1 more gallon of paint. In total, you would need 104 gallons of paint, which is the smallest whole number of gallons to cover the whole wall.

Guest Aug 2, 2023