A department store in your hometown charges 975 tax the stor

A department store in your hometown charges 9.75% tax; the store\'s location in your cousin\'s hometown only charges 7.75%tax. If a shopper 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).

Solution

Let the amount of pre-tax receipt be $ x. Then, we have the inequality 11.57 x 81.43.

Also, the difference in taxes at the two branches of the department store is 9.75 % (x) – 7.75 % (x) = 2% (x) = x *2/100 = x/50 = t ( say)

Since 11.57 x 81.43, therefore, we have 11.57/50 x/50 81.43/50 or, 0.23 t 1.63.

Thus, the difference in taxes is represented by the inequality 0.23 t 1.63. where t is the difference in taxes i.e. the difference in taxes is greater than or equal to 23 cents and less than or equal to $ 1.63

The graph of this inequality will be the portion between the two parallel lines (parallel to y –axis) t = 0.23 and t = 1.63 ( both the lines included). We may remember that t = x/50.

NOTE: we have rounded off to 2 decimal places as we were required to compute to the nearest cent.