Your roommate, Sarah, offered to buy groceries for you and your other roommate. The total bill was
$\$ 82 .$ She forgot to save the individual receipts but remembered that your groceries were $\$ 0.05$ cheaper than half of her groceries, and that your other roommates groceries were $\$ 2.10$ more than your groceries. How much was each of your share of the groceries?
Your roommate, John, offered to buy household supplies for you and your other roommate. You live
near the border of three states, each of which has a different sales tax. The total amount of money spent
was $\$ 100.75$ . Your supplies were bought with 5$\%$ tax, John's with 8$\%$ tax, and your third roommates with 9$\%$ sales tax. The total amount of money spent without taxes is $\$ 93.50 .$ If your supplies before tax were $\$ 1$ more than half of what your third roommate's supplies were before tax, how much did each of you spend? Give your answer both with and without taxes.
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