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 T(x) = 0.1x - 1500 for 15,000 < x ≤ 180,000 T(x) = 0.13x - 6900 for x > 180,000. Dakota has an income of $300,000. How much will they pay in taxes? Aliyah has an income of $10,000. How much will they pay in taxes? Enrique has an income of $70,000. How much will they pay in taxes? A politician proposes increasing the tax rate, but only on those making more than $330,000, to 19%. How much more will Enrique pay in taxes?

Solution

Let's break down the problem based on the tax formula given in the image.

The tax formula is:

0 & 0 \leq x \leq 15,000 \\ 0.1x - 1500 & 15,000 < x \leq 180,000 \\ 0.13x - 6900 & x > 180,000 \end{cases}$$ ### 1. Dakota's Income ($300,000) Dakota's income is $300,000, which falls in the range $$x > 180,000$$. So, we use the third part of the tax formula: $$T(300,000) = 0.13 \times 300,000 - 6900$$ Let's compute it: $$T(300,000) = 39,000 - 6,900 = 32,100$$ Dakota will pay **$32,100** in taxes. ### 2. Aliyah's Income ($10,000) Aliyah's income is $10,000, which falls in the range $$0 \leq x \leq 15,000$$. According to the first part of the tax formula: $$T(10,000) = 0$$ Aliyah will pay **$0** in taxes. ### 3. Enrique's Income ($70,000) Enrique's income is $70,000, which falls in the range $$15,000 < x \leq 180,000$$. So, we use the second part of the tax formula: $$T(70,000) = 0.1 \times 70,000 - 1,500$$ Let's compute it: $$T(70,000) = 7,000 - 1,500 = 5,500$$ Enrique will pay **$5,500** in taxes. ### 4. New Tax Proposal for Enrique The proposal suggests increasing the tax rate for incomes above $330,000 to 19%. However, Enrique's income is below $330,000, so **Enrique will not pay any additional taxes** under this proposal. --- Would you like to go into more detail or have any further questions? Here are some related questions: 1. How does a progressive tax system like this one benefit lower-income earners? 2. What would happen if Dakota's income were $180,000 exactly? 3. How would Enrique's tax change if his income increased to $200,000? 4. If Aliyah earned $16,000, how much tax would she pay? 5. What is the average tax rate Dakota pays on her income? **Tip**: Understanding tax brackets can help you calculate taxes for different income ranges more efficiently!

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Linear Functions
Tax Brackets
Algebra

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

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Suitable Grade Level

Grades 10-12

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