The number of buckets is directly proportional to the area and the thickness of the wall and inversely proportional to the amount of paint. Mathematically, we can write:

n = k · (a · t) / p

where k is the proportionality constant which we do not know.

We can calculate k with the given data: 5 2-gallon buckets, area of 100 square feet and thickness 3 inches:

k = (n · p) / (<span>a · t)
   = (5 </span>· 2) / (100 · 3) = 0.0333

Now that we know the constant, we can calculate the area that can be painted with 8 2-gallon buckets if the thickness is 6 inches:

a = (n · p) / (k<span> · t)
   = (8 </span>· 2) / (0.0333 · 6)
   = 80 ft²

Please, note that we made sure to have the exact same units of measurements than the previous case.

Therefore, the correct answer is an area of 80 ft².

4 0

3 years ago

Solve the system of equations x+y=-8 and -9x-6y=60 by combining the equations

TiliK225 [7]

Answer:

x = - 4 y = - 4

Step-by-step explanation:

x+y= - 8

-9x-6y=60

First, solve for x in the first equation:

x+y = - 8 Subtract y from both sides

x + y - y = -8 - y y cancels on the left

x = - 8 - y

Now plug in what you found for x into the 2nd equation and solve for y.

- 9x - 6y = 60

-9(- 8 - y) - 6y = 60 Multiply out

72 + 9y - 6y = 60

72 + 3y = 60 Subtract 72 from both sides

72 - 72 + 3y = 60 - 72 72 cancels on the left

3y = - 12 Divie both sides by 3

3y/3 = -12/3 3 cancels on the left because 3/3 = 1

y = -4

Now plug your answer for y back into the first equation to get x.

x + y = -8

x + (-4) = - 8 Add 4 to each side

x - 4 + 4 = - 8 + 4 4 cancels on the left

x = -4

x = - 4 and y = - 4

8 0

3 years ago