MATH SOLVE

4 months ago

Q:
# In American football, the playing field is 53.33 yards (yd) wide by 120 yards (yd) long. For a special game, the field staff want to paint the playing field orange. Of course, they will use biodegradable paint available for purchase in 25-gallon (gal) containers. If the paint is applied in a thickness of 1.2 millimeters (mm) in a uniform layer, how many containers of paint will they need to purchase?

Accepted Solution

A:

Answer: 68 containers of paint.Step-by-step explanation: First, we need to make the conversion from milimeters to yards. Knowing that: [tex]1\ yd=914.4\ mm[/tex] We get: [tex](1.2\ mm)(\frac{1\yd}{914.4\ mm})=1.31*10^{-3}\ yd[/tex] Knowing that the playing field is 53.33 yards wide by 120 yards long, and the paint will be applied in a thickness of 1.2 millimeters ([tex]1.31*10^{-3}\ yd[/tex]) , we can find the volume: [tex]V=(53.33\ yd)(120\ yd)(1.31*10^{-3}\ yd)=8.38\ yd^3[/tex] Now we must make the conversion from cubic yards to gallons. Since [tex]1\ yd^3=201.974\ gal[/tex], we get: [tex](8.38\ yd^3)(\frac{(201.974\ gal}{1\ yd})= 1,692.54\ gal[/tex] To find the number of containers of paint they will need to purchase, we must divide [tex]1,692.54\ gal[/tex] by [tex]25\ gal[/tex]: [tex]number\ of\ containers=\frac{1,692.54\ gal}{25\ gal}=67.70\approx68[/tex]