Math Problem Statement
In a certain country, the amount of income tax T on earnings of x dollars is computed according to the formula: T(x) = { 0 for 0 ≤ x ≤ 15,000, 0.1x - 1500 for 15,000 < x ≤ 180,000, 0.13x - 6900 for x > 180,000 }. How much tax will Dakota, Aliyah, and Enrique pay given their respective incomes of $300,000, $10,000, and $70,000? How much more will Enrique pay if a politician proposes raising the tax rate to 19% for incomes over $330,000?
Solution
The image contains a mathematical problem related to income tax, with a tax formula given in piecewise form. Let's solve the questions based on the given information.
Tax formula:
\begin{cases} 0 & \text{if } 0 \leq x \leq 15,000 \\ 0.1x - 1500 & \text{if } 15,000 < x \leq 180,000 \\ 0.13x - 6900 & \text{if } x > 180,000 \end{cases}$$ Where: - $$x$$ is the income in dollars. - $$T(x)$$ is the tax on income $$x$$. ### 1. Dakota has an income of $300,000. How much will they pay in taxes? Since Dakota's income is $300,000, which is greater than $180,000, we use the third formula: $$T(300,000) = 0.13(300,000) - 6900$$ Let's calculate: $$T(300,000) = 39,000 - 6900 = 32,100$$ Dakota will pay **$32,100** in taxes. ### 2. Aliyah has an income of $10,000. How much will they pay in taxes? Aliyah's income is $10,000, which is less than $15,000. According to the formula: $$T(10,000) = 0$$ Aliyah will pay **$0** in taxes. ### 3. Enrique has an income of $70,000. How much will they pay in taxes? Enrique's income falls in the range $$15,000 < x \leq 180,000$$, so we use the second formula: $$T(70,000) = 0.1(70,000) - 1500$$ Let's calculate: $$T(70,000) = 7,000 - 1500 = 5,500$$ Enrique will pay **$5,500** in taxes. ### 4. A politician proposes increasing the tax rate to 19% for those making more than $330,000. How much more will Enrique pay? Since Enrique earns $70,000, this tax increase proposal does not affect him, as the new tax rate is for incomes over $330,000. Therefore, Enrique will pay **$0 more** in taxes. --- Would you like further details or have any questions on these calculations? Here are some related questions for practice: 1. What would be the tax for someone earning $200,000? 2. If Dakota earned $150,000 instead, how much would the tax be? 3. Calculate the tax for an income of $20,000. 4. What would happen if the tax rate for those earning more than $500,000 was increased to 25%? 5. How would the formula change if there was an additional tax deduction of $2,000? **Tip**: Always check the range of the income carefully before applying the correct tax formula.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Income Tax Calculations
Linear Functions
Formulas
T(x) = 0 for 0 ≤ x ≤ 15,000
T(x) = 0.1x - 1500 for 15,000 < x ≤ 180,000
T(x) = 0.13x - 6900 for x > 180,000
Theorems
Piecewise function evaluation
Suitable Grade Level
Grades 10-12
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