Question

Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?

Answer 1

Someone help please!

Answer 2

How many feet in a yard?
How many inches in a foot?
How many cubic feet in a cubic yard?
We'll need these to answer the question.

Answer 3

This is the only thing that they gave me to answer it with
[1 foot = 12 inches; 1 yard = 3 feet]

Answer 4

So, there are 3 feet in a yard:
$$
\cfrac{3 \text{ feet}}{1 \text{ yard}}
$$
So 9 cubic feet is 1 cubic yard:
$$
\left (\cfrac{3 \text{ feet}}{1 \text{ yard}} \right )^3=\cfrac{9 \text{ feet}^3}{1 \text{ yard}^3}
$$
Make sense so far?

Answer 5

yes

Answer 6

The height of the concrete block is, since there is 12 inches in a foot:
$$
4 \text{ inches}\times\cfrac{1 \text{ foot}}{12 \text{ inches}}=\cfrac{4}{12} \text{ feet}\\
=\cfrac{1}{3}\text{feet}
$$
Make sense?

Answer 7

yupp.

Answer 8

k, so the volume of the concrete block is
$$
w\times l\times h\\
w \text{ feet }\times 8 \text{ feet}\times \cfrac{1}{3}\text {feet}\\
=\cfrac{8w}{3} \text{ cubic feet}
$$
But we need to convert to cubic yards, so since there are 9 cubic yards in a cubic foot:
$$
=\cfrac{8w}{3} \text{ cubic feet}\times \cfrac{9 \text{ cubic yards}}{1 \text{ cubic feet}}
\\=\cfrac{72w}{3}\text{ cubic yards}
$$
Ok?

Answer 9

oops, that's 9 cubic feet in a cubic yard, so...

Answer 10

Ok so what would you do next?

Answer 11

$$
=\cfrac{8w}{3} \text{ cubic feet}\times \cfrac{1 \text{ cubic yards}}{9 \text{ cubic feet}}
\\=\cfrac{8w}{27}\text{ cubic yards}
$$

Answer 12

So you would divide 27 by 8 and get 3.375? But round it to 3 right?

Answer 13

We know the total cost is $58.07 and the cost per cubic yard is $98, so then
$$
\cfrac{8w}{27}\text{ cubic yards}\times \cfrac{\text{\$}98}{1 \text{ cubic yard}}\\
=\cfrac{8\times98w}{27}=\text{\$}58.07\\
\implies w=\cfrac{58.07\times27}{8\times98}
$$
You'll just need to calculate and round to the nearest hundredth -- I'll let you do that :-)

Notice how all the units canceled at each step -- that's the key to solving all these problems.

That's it!

Answer 14

Thanks(:

Answer 15

yw