tax question find formulas

[santaclaus]

New York state income tax is based on taxable income, which is part of a person's total income. The tax owed to the state is calculated using the taxable income (not total income). In 2005, for a single person with a taxable income between $20,000 and $100,000, the tax owed was $973 plus 6.85% of the taxable income over $20,000.

a. Consider a lawyer whose taxable income is 80% of her total income, $x, where x is between $85,000 and $120,000. Write a formula T(x), the taxable income.

b. Write a formula for L(x), the amount of tax owed by the lawyer in part (a).

c. Use L(x) to evaluate the tax liability for x=85,000 and compare your results to part (a).


I'm stuck on a, so I can't do b or c.

[stapel_eliz]

a. Consider a lawyer whose taxable income is 80% of her total income, $x, where x is between $85,000 and $120,000. Write a formula T(x), the taxable income.

If "x" is the total income, and 80% (or 0.8) of that income "x" is "taxable", then what expression stands for eighty "percent of" the value of x? (Hint: "Of", in this context, means "times".)

Note: You may need to include restrictions on "x" in your formula: T(x) = (your expression for 0.8 times x), with 85,000 < x < 120,000.

In 2005, for a single person with a taxable income between $20,000 and $100,000, the tax owed was $973 plus 6.85% of the taxable income over $20,000.
b. Write a formula for L(x), the amount of tax owed by the lawyer in part (a).

To find the portion of income subject to the 6.85% tax, you'll need to subtract 20,000 from the value of T(x). You'll take 6.85% of this value (that is, multiply the expression by 0.065), and then add the base tax of $973. This is the L(x) they're looking for.

c. Use L(x) to evaluate the tax liability for x=85,000 and compare your results to part (a).

Plug "85,000" in for "x", and simplify to find the tax owed.

I'm not sure what they're wanting you to conclude from comparing the formula in part (a) to the numerical value in part (c)...?

[santaclaus]

thank you