Price of House, Commission

Date: 8/29/96 at 21:31:42
From: Amanda Z. Vega Frausto
Subject: Price of House, Commission

Dear Dr. Math,

Nina Perez is a real estate agent who recieves a commission of 
6 percent of the selling price of each house she sells.  The seller of 
the house pays Nina's commission out of the sale price and keeps 
the remainder.  What should be the sale price of each house if the 
seller wants to keep $61,000?

How do I solve this type of problem?

Crystal Vega

Date: 8/30/96 at 14:5:15
From: Doctor Jodi
Subject: Re: Price of House, Commission

Hi Crystal!  Since Nina is getting 6 percent of the sale price, the 
amount the seller wants to keep, $61,000 is 94% of the sale price.  
To find the sale price use an equation like

61, 000 = .94   x  sale_price

and then solve for the variable called "sale_price".

Does that make sense?

Let us know if you need more help!

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 8/30/96 at 10:2:52
From: Doctor Dave
Subject: Re: Price of House, Commission

Dear Crystal,

You need to understand that 6 percent of the sale price is simply a 
fancy way of saying 6/100 times the sale price.  If the realtor is 
getting 6S/100 and the seller is getting whats left, then the seller 
is getting 100S/100-6S/100 = 94S/100 or if you prefer 100percentS - 
6percentS = 94percentS. 

Now look at what we know: we know that the seller is getting $61,000 
and we discovered that this is the same as 94S/100. So, if we solve 
this equation (94S/100 = 61,000) for S we have our selling price.  
I'm sure you know how to solve this but I need the practice so I will 
show you anyway.
                             94s/100 = 61000
multiply both sides by 100/94      S = 6100 x 100/94
simplify                           S = 64893.62

Hint for solving any word problems; when ever you see a word problem 
in your homework or a test say to yourself "I love word problems" even 
if you don't mean it. If you say it enough you will start to believe 
it. Remember, I love word problems... I love word problems.

-Doctor Dave,  The Math Forum
 Check out our web site!