Question

"A department store in your hometown charges 9.75% tax; the stores location in your cousins hometown only charges 7.75% tax. If a shoppers 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 (to the nearest cent)"
I just need a start on how to do this.
Tbh, I've never heard of a pre-tax reciept. We get taxed on things that we pay, but is that the same thing as a pre-tax?

Also, at which location is this tax receipt being paid at? My hometown or my cousins hometown? (both of which has two different tax percentages)

Answer 1

Let x be the cost and the pre-tax receipt is between $11.57 and $81.43, so

11.57≤ x ≤ 81.43

Let y be the difference in taxes then,

11.57*(9.75/100 - 7.75/100) ≤ y ≤ 81.43*(9.75/100 - 7.75/100)  

=11.57*(0.0975 - 0.0775) ≤ y ≤ 81.43*(0.0975 - 0.0775)  

= 11.57*0.020 ≤ y ≤ 81.43*0.020

= 0.2314 ≤ y ≤1.6286

To the nearest cent, it is

0.23≤ y ≤1.62

Please find attached the graph.