Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Explain your work.
First Alexis needs to find the area she needs to paint. Alexis will need to paint two 30 foot - by - 50 foot walls and two 30 foot - by - 80 foot walls. $$2 \times 30 \textrm{ feet } \times 50 \textrm{ feet } = 3000 \textrm { square feet }$$ $$2 \times 30 \textrm{ feet } \times 80 \textrm{ feet } = 4800 \textrm { square feet }$$ Alexis will need to paint 3000 + 4800 = 7800 square feet.
Next, the table below shows how many square feet she can cover with different quantities of paint.
| Number of gallons of paint | Area covered |
|---|---|
| 1 | 420 |
| 5 | 2100 |
| 10 | 4200 |
| 15 | 6300 |
| 20 | 8400 |
20 gallons is a little more than she needs, so she can check 19 gallons and 18 gallons:
| Number of gallons of paint | Area covered |
|---|---|
| 1 | 420 |
| 5 | 2100 |
| 10 | 4200 |
| 15 | 6300 |
| 20 | 8400 |
| 19 | 7980 |
| 18 | 7560 |
18 gallons isn't quite enough and 19 gallons is a bit more than she needs. Since paint is usually sold in whole gallons, it makes sense for Alexis to buy 19 gallons of paint.
Finally, since paint costs $28 per gallon, the total cost will be $$19 \textrm{ gallons } \times $28 \textrm{ per gallon } = $532$$ It will cost Alexis $532 to paint the barn.
Commentary
The purpose of this task is to provide students an opportunity to use mathematics addressed in different standards in the same problem.