Answer:
[tex]\large \boxed{\$532}[/tex]
Step-by-step explanation:
Assume the barn is 80 ft long, 50 ft wide, and 30 ft high
1. Area to paint
They will be painting two sides and two ends.
The sides are 80 ft × 30 ft.
The ends are 50 ft × 30 ft,
Area of sides = 2 × 80 ft × 30 ft = 4800 ft²
Area of ends = 2 × 50 ft × 30 ft = 3000 ft²
Total area = 7800 ft²
2. Amount of paint needed
One gallon covers 420 ft².
[tex]\text{Amount of paint} = \text{7800 ft}^{2} \times \dfrac{\text{1 gal}}{\text{420 ft}^{2}} = \text{18.6 gal}[/tex]
They usually sell barn paint in whole gallons. Alexis will have to buy 19 gal of paint to cover the whole barn.
3. Total Cost
It costs $28 for one gallon of paint,
[tex]\text{Total cost} = \text{19 gal} \times \dfrac{\$28}{\text{1 gal}} = \mathbf{\$532}\\\\\text{It will cost $\large \boxed{\mathbf{\$532}}$ to paint the barn.}[/tex]
