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.
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
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.
To find the cost of 950 bricks, we need to calculate the total weight in ounces and then multiply it by the cost per ounce:
Step 1: Calculate the volume of one brick.
Since the brick is in the shape of a right rectangular prism, we can find the volume by multiplying its length, width, and height:
Volume of one brick = 7 1/2 in * 2 3/4 in * 2 1/2 in
Convert the given dimensions to fractions:
7 1/2 in = 15/2 in
2 3/4 in = 11/4 in
2 1/2 in = 5/2 in
Now we can calculate the volume of one brick:
Volume of one brick = (15/2 in) * (11/4 in) * (5/2 in)
Step 2: Calculate the weight of one brick.
The weight of one brick is equal to its volume multiplied by the weight per cubic inch:
Weight of one brick = Volume of one brick * Weight per cubic inch
Given that the weight per cubic inch is 0.04 ounces per cubic inch, we have:
Weight of one brick = (15/2 in) * (11/4 in) * (5/2 in) * 0.04 ounces
Step 3: Calculate the total weight of 950 bricks.
The total weight of 950 bricks will be 950 times the weight of one brick:
Total weight of 950 bricks = 950 * Weight of one brick
Step 4: Calculate the cost of 950 bricks.
The cost of 950 bricks is equal to the total weight of 950 bricks multiplied by the cost per ounce:
Cost of 950 bricks = Total weight of 950 bricks * Cost per ounce
Given that the cost per ounce is $0.09, we have:
Cost of 950 bricks = Total weight of 950 bricks * $0.09
Now we can calculate the solution:
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 $\boxed{\$211.61}$.