1. ## Calculating taxable income

I just finished working out this problem and I'm not very sure if I did it correctly

For a) The formula I wrote out is f(x) = 0.0685(x) + 973 which would give me a taxable income of 4261. Can you check if the formula is correct?

For b) Since they didn't give me a real income to go on, I just wrote out the formula for whatever the lawyer's income could be which is T(x) = 0.8(x), x = income. I don't know if that is correct by multiplying it by 0.8 or should the formula be T(x) = x - 20000, x = income. Please check if this is correct.

For c) L(x) = (T(x) - 20000)(0.0685) + 973
Please check if this formula is correct

For d) I just used the above formula and placed in 85000 for x.

2. Originally Posted by nox16
I just finished working out this problem and I'm not very sure if I did it correctly

For a) The formula I wrote out is f(x) = 0.0685(x) + 973 which would give me a taxable income of 4261. Can you check if the formula is correct?
No, that is not correct. The percentage only applies to that part of the taxable income which more than \$20000. You should use f(x)= 0.0685(x- 20000)+ 973.

For b) Since they didn't give me a real income to go on, I just wrote out the formula for whatever the lawyer's income could be which is T(x) = 0.8(x), x = income. I don't know if that is correct by multiplying it by 0.8 or should the formula be T(x) = x - 20000, x = income. Please check if this is correct.
Yes, the taxable income is T(x)= 0.8x. Assuming that is between 20000 and 100000, then the tax would be 0.0685(.8x- 20000)+ 973.

For c) L(x) = (T(x) - 20000)(0.0685) + 973
Please check if this formula is correct
Yes, although it would be better to write explicitely that
L(x)= 0.0685(0.8x- 20000)+ 973.

For d) I just used the above formula and placed in 85000 for x.
Yes, that would be correct.