Help on one math problem?

Question

A simple income tax schedule is shown.

Income Tax
up to $20,000 15% of income
More than $20,000 $3,000 + 28% of income in excess of $20,000

a. for what incomes is the tax at least 20% of total income?
b. for what incomes is the tax at most 25% of total income?
c.Tony's employer wants him to work overtime hours in December. If Tony does his, his income for the year will barely exceed $20,000. Tony is worried that, since the additional income will change his tax bracket, he will actually lose money that is, his additional taxes will exceed his added income, by working more hours. Are his fears justified?

Answer 1

a) 3000 + 0.28(x-20000) = x/5
3000 + 0.28x - 5600 = x / 5
0.28x - 2600 = x / 5
1.4x - 13000 = x
0.4x = 13000
x = $32,500 and up

b) 3000 + 0.28(x-20000) = x/4
3000 + 0.28x - 5600 = x / 4
0.28x - 2600 = x / 4
1.12x - 10400 = x
0.12x = 10400
x = $81,250 and less

c) No, The tax on the first $20,000 is $3000
Dollars after the first $20,000 are taxed at 28%.

Answer 2

If you make exactly $20,000 your tax will be $3,000
Let x = your income
Then tax = 3000 +.28(x-20000) = .28x -2600
.28x -2600 = .2x
.08x - 2600
x = 32,500 would be 20% 0f total income
.28x-2600 = .25x
.03x = 2600
x = 86,666.67= income taxed at 25%

If Tony earns 20,200 his taxes will be 3000+.28(200) =3056.
So he made 200 more but gets to keep $144 which is 72% of his additional earnings. His fears are not justified

Answer 3

Yeah right. Like I'm gonna do your homework for you on Sunday night. NOT.