For an income over $10000, a state charges a fixed tax of $300 plus 6.5% of the income in excess of $10000.
A) Calculate the income tax for a person with an income of $80000.
B) If Mike paid $7508.50. What was Mike's income?

Question

For an income over $10000, a state charges a fixed tax of $300 plus 6.5% of the income in excess of $10000. 
A) Calculate the income tax for a person with an income of $80000.
B) If Mike paid $7508.50. What was Mike's income?

mathstudent55 · Answer

Call income x.
Then, income in excess of 10,000 is x - 10,000.
Fixed tax is 300.
Tax on excess is 6.5% of excess, or 6.5% of (x - 10,000) = 0.065(x - 10,000)
Total tax, T = 300 + 0.065(x - 10,000)
A) use the above formula for tax and plug in x = 80,000
B) let T = 7508.5, plug that into the eqaution and solve for x.

spareb665 · Answer

so 300 + 0.065(80000-10000) =4850?

mathstudent55 · Answer

Correct.

mathstudent55 · Answer

Part B)
The tax is 7508.50, that equals T
You are looking for x
7508.50 = 0.065(x-10000)