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?

[1 foot = 12 inches; 1 yard = 3 feet]

Answer 1

First determine how many cubic yards Matt bought.

Answer 2

I cant really understand how to solve it. I tried several times but nothing worked

Answer 3

All the time, i am getting confused

Answer 4

Ok if he spent $ 58.07 and the price of concrete is $98.00 per cubic yard. Hw many cubic yards did he buy?

Answer 5

do we need to subtract those two value to find it

Answer 6

?

Answer 7

It is a ratio....\[\frac{ 98 }{ 1 } = \frac{ 58.07 }{ x }\] You need to cross multiply to solve for x. Are you familiar with this?

Answer 8

yes

Answer 9

Ok solve for x and let me know.

Answer 10

98x = 58.07

Answer 11

98x/98 = 58.07/98 = 0.5925510204082

Answer 12

then?

Answer 13

OK so he bought .5925 cubic yards. Looking at the equation we are probably going to have to convert this to cubic inches. So you many cubic feet in a cubic yard?

Answer 14

3 feet

Answer 15

1 yard = 3 feet

Answer 16

Think about a cube that is one yard high, one yard wide and one yard long. So what be in cubic feet?

Answer 17

8 feet long and 4 inches high

Answer 18

is it this one your saying?

Answer 19

I am confused here bit :(

Answer 20

is it 27 cubic inches?

Answer 21

Volume of a cube is Length x width x height. If a cube is 1 cubic yard it is Length =1 yard and its width = 1 yard and its height = 1 yard. Thus we get 1 x 1 x1 = 1.
Now we need to covert to inches. If there are 36 inches in a yard, we say the length = 36 inches and the width = 36 inches and the height = 36 inches. So a cubic yard in inches would be 36 x 36 x 36 = ? Does this help?

Answer 22

Not quite

Answer 23

did you mean 8 inches to multiply three times?

Answer 24

sorry 4 inches

Answer 25

like 4*4*4 = 64 inches

Answer 26

There you go. Now a cubic yard is how many inches on both sides. Don't use numbers from your question, ask youself how many inches in a yard?

Answer 27

both side I think 64 inches. As you said 1 yard = 27. But I dont know how to convert inches to yard

Answer 28

There are 36 inches in a yard. So a cubic yard is 36 x 36 x 36 which equals ???

Answer 29

46656

Answer 30

Great!!! Now earlier you figured he bought .5926 cubic yards. If 46656 cubic inches = 1 cubic yard. How many cubic inches did he buy? \[\frac{ 1 }{ 46656 }=\frac{ .5926 }{ ? }\]

Answer 31

x

Answer 32

am I right?

Answer 33

No 36

Answer 34

Cross multiply like you did above.

Answer 35

isnt it?

Answer 36

okay

Answer 37

So we now know Matt bought 27648 cubic inches of concrete. Now we need to develop a formula. The formula for finding volume is length x width x height = volume. So let's plug in the numbers. What is the length in inches of the driveway.

Answer 38

so we multiply with 4 inches and 8 feet?

Answer 39

Close..You have two of the three numbers you need. You do not know the width that's what we are trying to solve. What is the length of the 8 foot long driveway in inches?

Answer 40

4 inches

Answer 41

8 feet long = 4 inches????

Answer 42

I am really sorry trouble, I am really struggling with it. That's why, it is taking long

Answer 43

Not a problem....8 feet equals 96 inches.. 12 inches in a foot x 8 = 96. So we have one number of our formula 96 x height x width = Volume. Looking at the question what is given as the height of the driveway?

Answer 44

4 inches high

Answer 45

Great!!!! Now we have two numbers of the formula 96 x 4 x width = Volume. Now they want us to solve for width so that is not given. Earlier we figured the volume as 27648. So our formula looks like this

96 x 4 x width = 27648. Now you need to solve for the width. Can you do that or do I need to help?

Answer 46

I am not sure, would mind help me here too? Can you tell me how do find 8 feet = 96 inch?

Answer 47

There are how many inches in 1 foot?

Answer 48

12

Answer 49

If there are 8 feet and there are 12 inches in a foot. Then 8 (number of feet) x 12(inches in a foot) = 96

Answer 50

Oh I get now how you got 96

Answer 51

Back to the original problem. Our solution looks like this

96 x 4 x width = 27648. We need to isolate the unknown (width) on one side of the equation. So let's start out by multiplying 96 x 4 . What do you get?

Answer 52

384

Answer 53

So our equation now looks like this 384 x width = 27648. Now can you solve for the width?

Answer 54

I am trying :)

Answer 55

I know you are

Answer 56

72

Answer 57

Winner winner chicken dinner... Excellent. We now know the width is 72 inches...how many feet is that???

Answer 58

72*1/12 = 6 feet.
Thanks so so much for teaching me so hard!!! :)
I was having really hard time to understand it

Answer 59

You did great and it was a pleasure... :-}

Answer 60

It is all because of you, entire credit goes to you :) thanks a lot!!!