A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 7 1/2 ​ in by 2 3/4 ​ in by 2 1/2 ​ in. If the bricks weigh 0.04 ounces per cubic inch and cost $0.09 per ounce, find the cost of 950 bricks. Round your answer to the nearest cent.

Answer 1

The volume of one brick is:

$$7\frac{1}{2}\text{ in}\cdot2\frac{3}{4}\text{ in}\cdot2\frac{1}{2}\text{ in}=61.875\text{ cubic inches}$$

The weight of one brick is:

$$61.875\text{ cu in}\cdot0.04\text{ oz/cu in}=2.475\text{ ounces}$$

The cost of one brick is:

$$2.475\text{ oz}\cdot \$0.09/\text{oz}=\$0.22275$$

Therefore, the cost of 950 bricks is:

$$950\text{ bricks}\cdot\$0.22275/\text{brick}=\$211.61$$

Rounding to the nearest cent, the answer is $\boxed{\$211.61}$.

Answer 2

AAAaannndd the bot gets it wrong yet again!
Lots of mistakes, such as
(7 1/2 * 2 3/4 * 2 1/2) = 51.56 in^3/brick, not the 61.875 you figured.

The upshot is that

950 brick * $0.09/oz * 0.04oz/in^3 * (7 1/2 * 2 3/4 * 2 1/2) in^3/brick = $176.34

Answer 3

I apologize for my mistake in the previous answer. Thank you for correcting it. You are correct that the volume of one brick is 51.56 cubic inches, not 61.875 cubic inches.

Using the correct volume of one brick, the weight of one brick is:

$$51.56\text{ cu in}\cdot0.04\text{ oz/cu in}=2.0624\text{ ounces}$$

The cost of one brick is:

$$2.0624\text{ oz}\cdot \$0.09/\text{oz}=\$0.18562$$

Therefore, the cost of 950 bricks is:

$$950\text{ bricks}\cdot\$0.18562/\text{brick}=\$176.34$$

Thank you for bringing the mistake to my attention.