# a department store in your hometown charges 9.75% tax the store's location in your cousin's hometowm only charges 7.25% tax.if a shopper's pre-tax receipt is between $11.57 and $81.43 write and...

a department store in your hometown charges 9.75% tax the store's location in your cousin's hometowm only charges 7.25% 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 (to the nearest cent) write the inequality for a graph.

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### 1 Answer

Pre-tax the amounts vary from $11.57 and $81.43. This means in your hometown, the tax will be from `0.0975 times 11.57 = 1.13` to `0.0975 times 81.43 = 7.94` . In your cousin's hometown, the tax varies from `0.0725 times 11.57=0.84` to `0.0725 times 81.43=5.90` . In both cases, the tax will vary linearly with the pre-tax purchase.

An inequality that describes the taxes for your hometown is:

`1.13 <= t <= 7.94`

and the inequality for your cousin's hometown is:

`0.84 <= t<=5.90`

An inequality that describes the difference in taxes is:

`1.13 - 0.84 <= d<=7.94 - 5.90` simplifies to:

`0.29<=d<=2.04`

**The inequality of the difference in taxes is `0.29<=d<=2.04` .This inequality can be graphed below:**