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Question 1005924: A dept. store in your town charges9.75% tax: the store's location in your cousin
town only charges 7.75% tax. If a shopper's pre-tax receipt is between $11.57 and $81.43, write and graph a compound inequality that describes the difference in taxes paid for the two locations.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! It is too bad that the sales tax is as high as 9.75% in your town.
It would be a good idea to do as much of your buying as possible in your cousin's town.
If the pre-tax total , in $, of a purchase is  ,
the tax would be  in your town, and  in your cousin's town.
The difference is
 ,
a 2% savings.
"The shopper's pre-tax receipt is between $11.57 and $81.43" translates as
 .
That is a compound inequality.
It is called a compound inequality,
because it is made of two inequalities,
 , written together.
If you multiply both sides of an inequality times the same positive number,
you get an equivalent inequality, and do not need to reverse the inequality.
So, from  you get
 --->
Applying that to both parts of the compound inequality, you get
 ---> ---> .
because the total price, and hence the tax, would be rounded to the nearest $0.01,
 would be rounded to  and
 would be rounded to  .
I would say that the compound inequality expected is
 ,
maybe with or without the "$",
maybe giving a cute one-letter name to "savings".
A way to graph that would be
I assume something like that is what was expected,
but different teachers have different format preferences,
and different ways to fuzzily explain what they want.
It is sometimes hard to guess what the teacher expects,
even if you have been in class, paying attention.
Good luck!
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