Algebra story problem.. Compound inequality and graphing

Question

A fast food restaurant incorrectly programs its registers to charge 9.5% sales tax. If each order is at least $1.99, and the largest order for the day is $16.57, write and graph a compound inequality that describes the amount that a customer is overcharged. (To the nearest cent)

Answer 1

Hi Michael.

 

We have a tax rate of 9.5% (0.095 as a decimal).

 

The smallest sale is $1.99

The largest sale is $16.57

 

The tax on the smallest sale is

1.99 x .095 = $0.19

 

The tax on the largest sale is 

16.57 x .095= $1.57

 

Since prices can be any amount between $1.99 and $16.57, then the tax charged can be any amount between $0.19 and $1.57.

 

Therefore the compound inequality is

0.19 ≤ t ≤ 1.57

 

And graphing it (This is a bit tricky in this venue).

 

<--------|------•-------------------|------------•----->

           $0   $0.19               $1.00          $1.57

 

OK, the "graph" doesn't look exactly the way I want it to look, so let me explain.

We have a number line.

A darkened circle on the point 0.19 and another darkened circle on the point 1.57.  The part of the line between these two point is darkened as well.