Determine Cubic Feet Used: For one quarter, a home owner's water bill was $9.38.

K

KWF

Junior Member
Joined
Feb 19, 2010
Messages
204
For one quarter, a home owner's water bill was $9.38. The water company charges $6.50 for the first 1,200 cubic feet or less, and $0.40 per hundred for the next 3,600 cubic feet. How many cubic feet of water did the home owner use during that period?

Answer: 1,920 cubic feet

Here is my solution: What cubic feet * $0.40/100 cubic feet = ($9.38 - $6.50) + 1,200 cubic feet?

Is there a better solution than mine?
 
KWF said:
For one quarter, a home owner's water bill was $9.38. The water company charges $6.50 for the first 1,200 cubic feet or less, and $0.40 per hundred for the next 3,600 cubic feet. How many cubic feet of water did the home owner use during that period?

Answer: 1,920 cubic feet

Here is my solution: What cubic feet * $0.40/100 cubic feet = ($9.38 - $6.50) + 1,200 cubic feet?

Is there a better solution than mine?
Click to expand...
Not better - but formed slightly differently:

Total cft. of water used = W

Excess water used = W - 1200

Then:

6.5 + (W-1200)/100 *0.4 = 9.38

0.004 * W = 9.38 - 6.5 + 4.8 = 7.68

W = 7.68/0.004 = 1.92 * 10^3 cft

Check:

excess water = 1920 - 1200 = 720

Charge = 6.5 + 7.2 * 0.4 = 6.5 + 2.88 = 9.38 ← checks
 
Well, you ended up with the right answer, so that's good. But your method is absolutely incorrect, and it's very unclear as to what you actually did. Let's temporarily put aside numbers and look only at the units of your method:

  • (Cubic Feet) * (Dollars)/(Cubic Feet) = (Dollars) + (Cubic Feet)
  • (Dollars) = (Dollars) + (Cubic Feet)

It should be immediately obvious why this cannot ever be the case, regardless of what numbers are attached to those units. This equation has no solution, simply because it makes no sense. Going forward, you need to be more careful in your work, because if your teacher (and later in life, your boss) can't understand your work and your thought process, that's no good. That all said, you did get the right answer in the end, so what I think you really meant to show with your workings is something like the following:

I first solved for the amount of cubic feet over 1200 by using this equation:

\(\displaystyle x \text{ cubic feet} \cdot \dfrac{$0.40}{100 \text{ cubic feet}} = $9.38 - $6.50\)

Which gave me \(\displaystyle x = 720\). Therefore, my answer is:

\(\displaystyle 720 \text{ cubic feet} + 1200 \text{ cubic feet} = 1920 \text{ cubic feet}\)
Click to expand...
 
Last edited:
KWF said:
For one quarter, a home owner's water bill was $9.38. The water company charges $6.50 for the first 1,200 cubic feet or less, and $0.40 per hundred for the next 3,600 cubic feet. How many cubic feet of water did the home owner use during that period?

Answer: 1,920 cubic feet

Here is my solution: What cubic feet * $0.40/100 cubic feet = ($9.38 - $6.50) + 1,200 cubic feet?

Is there a better solution than mine?
Click to expand...
Well, the main problem I have with it is that I don't know how to add "cubic feet" to "dollars"!

$9.38 is larger than $6.50 so the amount of water was more than 1200 cubic feet. The extra payment is 9.38- 6.50= $2.88. That is 2.88/(0.40)= 7.2 so there must have been 7.2 additional 100 cubic feet. The total is 1200+ 720= 1920 cubic feet.
 
KWF said:
For one quarter, a home owner's water bill was $9.38. The water company charges $6.50 for the first 1,200 cubic feet or less, and $0.40 per hundred for the next 3,600 cubic feet. How many cubic feet of water did the home owner use during that period?

Answer: 1,920 cubic feet

Here is my solution: What cubic feet * $0.40/100 cubic feet = ($9.38 - $6.50) + 1,200 cubic feet?

Is there a better solution than mine?
Click to expand...
The left hand side, What cubic feet * $0.40/100 cubic feet, has $ for the units (cubic feet cancel out) while the right hand side has $ + cubic feet as its units. Of course this is not right. You have something like $7 = $4 + 11 cubic feet. Does that make sense to you?
 
Last edited:
ksdhart2 said:
Well, you ended up with the right answer, so that's good. But your method is absolutely incorrect, and it's very unclear as to what you actually did. Let's temporarily put aside numbers and look only at the units of your method:

  • (Cubic Feet) * (Dollars)/(Cubic Feet) = (Dollars) + (Cubic Feet)
  • (Dollars) = (Dollars) + (Cubic Feet)

It should be immediately obvious why this cannot ever be the case, regardless of what numbers are attached to those units. This equation has no solution, simply because it makes no sense. Going forward, you need to be more careful in your work, because if your teacher (and later in life, your boss) can't understand your work and your thought process, that's no good. That all said, you did get the right answer in the end, so what I think you really meant to show with your workings is something like the following:
Click to expand...

Thank you for your reply and solution!

There is a typographical error that you overlooked. The $0.04 should be $0.40. I could not get you solution to produce the correct answer until I realized that the $0.04 should be $0.40. Thanks again and do not think I am being too nit picky.
 
KWF said:
Thank you for your reply and solution!

There is a typographical error that you overlooked. The $0.04 should be $0.40. I could not get you solution to produce the correct answer until I realized that the $0.04 should be $0.40. Thanks again and do not think I am being too nit picky.
Click to expand...

Oh, whoops! Yes, I made a small typo. Sorry about that. I'm glad you figured out what I meant though, and it didn't lead you too far astray. I'll go back and fix it, just for posterity's sake.
 
ksdhart2 said:
Oh, whoops! Yes, I made a small typo. Sorry about that. I'm glad you figured out what I meant though, and it didn't lead you too far astray. I'll go back and fix it, just for posterity's sake.
Click to expand...

I have another calculation regarding the cubic feet question. Is it mathematically logical?

1200 cubic feet + ($9.38-$6.50)/($0.40/100 cubic feet * 3600 cubic feet) * 3600 cubic feet = 1920 cubic feet

I think that this simplifies to 1200 cubic feet + (1/5 * 3600 cubic feet) = 1920 cubic feet

I know that your calculation is much better, but I am curious to know whether or not this one is also correct. I think that the units cancel properly, but I'm not entirely sure.
 
Denis said:
Remove the 1200 part:
water bill for $2.88, representing .40 per hundred cubic feet;
how many cubic feet?
2.88 / .40 * 100 = 720
Over and out!
Click to expand...

That is a nice, concise solution, but the 1200 cubic feet need to be used in your solution in order to get the answer 1920 cubic feet.

1200 cubic feet + ($2.88/$0.40 * 100) = 720 cubic feet + 1200 cubic feet = 1920 cubic feet
 
KWF said:
For one quarter, a home owner's water bill was $9.38. The water company charges $6.50 for the first 1,200 cubic feet or less, and $0.40 per hundred for the next 3,600 cubic feet. How many cubic feet of water did the home owner use during that period?

Answer: 1,920 cubic feet

Here is my solution: What cubic feet * $0.40/100 cubic feet = ($9.38 - $6.50) + 1,200 cubic feet?

Is there a better solution than mine?
Click to expand...

What cubic feet * $0.40/100 cubic feet = ($9.38 - $6.50) + 1,200 cubic feet? ..... This equation is incorrect

It is dimensionally incorrect - as explained above.
 
You must log in or register to reply here.
Top