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polet [3.4K]
2 years ago
13

A ballasted roof is flat and covered with gravel to hold the roofing material in place. Adam plans to cover the roof in the diag

ram with gravel.
30 ft.
21 ft.
13 ft.
57 ft.
27 ft.
52 ft.
The area that Adam plans to cover with gravel is
weight of gravel on the roof will be
If the weight of the gravel is 12 pounds per square foot, the total
ling
2,702 square feet
Next
2,374 square feet
2,222 square feet
2,031 square feet

Mathematics
1 answer:
Yuri [45]2 years ago
5 0

Answer:

Area = 2,031ft^2

Total weight of gravel on the roof = 24,372 pounds

Step-by-step Explanation:

The area Adams planned to cover with gravel can be divided into 3 rectangles as shown in the diagram attached.

We would have 3 rectangles. See the attachment below to check out how we arrive at the dimensions of the 3 rectangles.

Area of rectangle = L*W

Area to be covered by gravel = area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area to be covered with gravel = (30*17) + (13*9) + (52*27)

Area = (30*17) + (13*9) + (52*27) = 2,031ft^2

Total weight of gravel on the roof = 12 pounds per square foot multiplied by total area of the roof to be covered = 12 * 2031 = 24,372 pounds

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For every 1 cup of blue paint, \frac{10}{4} cups of red paint are needed

For every 1 cup of red paint, \frac{4}{10} cup of blue paint is needed

For every 4 cups of red paint, \frac{16}{10} cups of blue paint are needed

<em><u>Solution:</u></em>

Given that, there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint

Therefore, ratio is

Red : blue = 3\frac{1}{3} : 1\frac{1}{3}\\\\Red : blue = \frac{10}{3} : \frac{4}{3}

<h3><u>For every 1 cup of blue paint, ___ cups of red paint are needed</u></h3>

Let "x" be the cups of red paint needed

Then we get,

\frac{10}{3} : \frac{4}{3}\\\\x : 1

This forms a proportion

1 \times \frac{10}{3} = \frac{4}{3} \times x\\\\x = \frac{10}{4}

Therefore, 10/4 cups of red are needed for 1 cup of blue

<h3><u>For every 1 cup of red paint, ___ cup of blue paint is needed</u></h3>

Let "x" be the cups of blue paint needed

Then, we get

\frac{10}{3} : \frac{4}{3}\\\\1 : x

This forms a proportion

\frac{10}{3} \times x = \frac{4}{3} \times 1\\\\x = \frac{4}{10}

Thus, 4/10 cups of blue are needed for 1 cup of red paint

<h3><u>For every 4 cups of red paint,___ cups of blue paint are needed</u></h3>

Let "x" be the cups of blue paint needed

Then, we get

\frac{10}{3} : \frac{4}{3}\\\\4 : x

This forms a proportion

\frac{10}{3} \times x = \frac{4}{3} \times 4\\\\x = \frac{16}{10}

Thus 16/10 cups of blue paint are needed for every 4 cups of red paint

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