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### Cost of Cleaning a Building

```Date: 07/03/2003 at 08:44:29
From: Carl
Subject: Cleaning a building

Hi,

I own a cleaning company and am having trouble figuring cost per
square foot.  If I clean a 3200 square foot building five nights per
week for a sum of \$575.00 per month, what is the cost per square foot?

I also need a formula for figuring out future bids for buildings with
different square footage and different numbers of days per month.

Regards,
Carl
```

```
Date: 07/03/2003 at 11:38:45
From: Doctor Ian
Subject: Re: Cleaning a building

Hi Carl,

If you clean a 3200 square foot building five nights per week for a
sum of \$575.00 per month, the cost per square foot would be

575 dollars    575
------------ = ---- dollars per square foot
3200 sq feet   3200

For formulas for future buildings, as in the example above, you divide
the number of dollars you're going to charge by the number of square
feet to get the cost per square foot.

I'm not sure how days per month figures into it, but if you'd like to
tell me more, perhaps I can help with that.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 07/03/2003 at 16:39:41
From: Carl
Subject: Cleaning a building

Thanks for you response.

I currently clean a building that is 3200 sq.ft., 5 times per week,
for a sum of \$575.00 per month. I am trying to bid another building
that is 4000 sq.ft. and they only want it cleaned once a week. So I
need to figure out a formula of cost per square foot per day so I can
multiply that figure times the days and the square feet to come
up with a comparable quote for this building.

I tried 3200 sq. ft. divided by \$575.00 divided by 20 days and came up
with .28 cents per square foot, but when I reversed the problem to
check my math it did not work.

If it helps, I also clean a 2500 square foot building 5 times a week
for \$350.00 and a 1008 square foot building twice a week for \$300.00,
but all pricing thus far has been done by guess and it is time to come
up with a formula.

Carl
```

```
Date: 07/03/2003 at 19:48:17
From: Doctor Ian
Subject: Re: Cleaning a building

Hi Carl,

Is the idea that you want to get the same amount of money for the same
amount of work?  If so, then this ratio

cost
----------------
area * cleanings

has to remain constant. For example, suppose you increase the area
from 3200 sq ft to 4000 sq ft, but cut the number of cleanings by a
factor of 5 (from 5 times per week to 1 time per week).  Then

575         ?
-------- = --------
3200 * 5   4000 * 1

To solve this, you can multiply both sides by the denominator on the
right to get

575 * 4000 * 1
-------------- = \$143.75
3200 * 5

To work it out using a different building, the formula is

(current cost) * (new area) * (new cleanings per week)
------------------------------------------------------
(old area) * (old cleanings per week)

Let's see how that works out using your other buildings.  For the
first one, we get

350 * 4000 * 1
-------------- = \$112
2500 * 5

For the second, we get

300 * 4000 * 1
-------------- = \$595.24
1008 * 2

That looks high, but consider that you're cleaning less than half the
area (1008 vs. 2500), less than half as many times (2 times vs. 5
times) for almost the same money (\$300 vs. \$350).

It looks as if you can put in a pretty wide range of bids!

Anyway, that's the formula.  Let me know if you had trouble following
what I did, or using it yourself.

I hope this helps!

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 07/15/2003 at 11:23:47
From: Carl
Subject: Thank you (Cleaning a building)

Thanks for taking the time to solve my problem.

Carl
```
Associated Topics:
Middle School Ratio and Proportion
Middle School Word Problems

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