### Understanding the Calculation of Business Bonuses and TaxesA business has a gross income of **$1.14 million**. The CEO is promised a bonus of **20%** of the net income, which is the income after taxes. The bonus is not subject to taxes, since it is considered an operating expense. The goal is to find the profit after paying the bonus and taxes. Let **B** be the amount on which the bonus is based, and **T** be the amount on which taxes are calculated, both in millions of dollars.#### (a) Express Taxes Paid in Terms of TThe taxes paid are calculated as:\[ 0.2T \]#### (b) Expressing Gross IncomeThe gross income of **$1.14 million** equals the amount **B** on which the bonus is based, plus the taxes paid. Therefore, the equation becomes:\[ 1.14 = B + 0.2T \]#### (c) Express the Bonus in Terms of BThe bonus is expressed as:\[ 0.2B \]#### (d) Express Gross Income in Terms of T and BThe gross income is also equal to the amount **T** on which taxes are based plus the bonus paid:\[ 1.14 = T + 0.2B \]#### (e) Solve the System of Equations- From part (b): $ 1.14 = B + 0.2T $- From part (d): $ 1.14 = T + 0.2B $Solve these equations to find values for **T** and **B** (currently not filled).#### (f) Determine Bonus and Taxes- How much is the bonus?- How much is paid in taxes?This section requires solutions for the variables to determine the specific amounts for the bonus and taxes. The answer fields are currently blank. **Educational Content: Calculating Financial Insights****Financial Calculations Interface**1. **Bonus Calculation:** - Query: "How much is the bonus?" - Input Field: Enter the bonus amount in millions of dollars.2. **Tax Calculation:** - Query: "How much is paid in taxes?" - Input Field: Enter the tax amount in millions of dollars.3. **Profit Calculation:** - Query: "How much profit is left over?" - Input Field: Enter the remaining profit in millions of dollars.Additionally, users can see:- A labeled field for `T`, currently set at 1.14 with an error indicated by a red cross.- An unlabeled field for `B`.At the bottom, there is a help option available:- Link/Button: "Need Help?" followed by a "Read It" button for additional guidance.

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Description: ### Understanding the Calculation of Business Bonuses and TaxesA business has a gross income of **$1.14 million**. The CEO is promised a bonus of **20%** of the net income, which is the income after taxes. The bonus is not subject to taxes, since it

For part e: The objective here is to find the value of T, and B by solving the equation in b and d.…

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A business has a gross income of $1.14 million. It has promised to pay the CEO a bonus of 20% of net income, which is income after taxes. But the bonus is not subject to taxes because the bonus is an operating expense. The total tax owed is 20% of gross income less the bonus. Our goal is to find the company profit after the bonus and taxes are paid. Let B be the amount on which the bonus is based, and let T be the amount on which taxes are calculated, both in millions of dollars.

A business has a gross income of $1.14 million. It has promised to pay the CEO a bonus of 20% of net income, which is income after taxes. But the bonus is not subject to taxes because the bonus is an operating expense. The total tax owed is 20% of gross income less the bonus. Our goal is to find the company profit after the bonus and taxes are paid. Let B be the amount on which the bonus is based, and let T be the amount on which taxes are calculated, both in millions of dollars.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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### Understanding the Calculation of Business Bonuses and Taxes

A business has a gross income of **$1.14 million**. The CEO is promised a bonus of **20%** of the net income, which is the income after taxes. The bonus is not subject to taxes, since it is considered an operating expense. The goal is to find the profit after paying the bonus and taxes.

Let **B** be the amount on which the bonus is based, and **T** be the amount on which taxes are calculated, both in millions of dollars.

#### (a) Express Taxes Paid in Terms of T

The taxes paid are calculated as:

\[ 0.2T \]

#### (b) Expressing Gross Income

The gross income of **$1.14 million** equals the amount **B** on which the bonus is based, plus the taxes paid. Therefore, the equation becomes:

\[ 1.14 = B + 0.2T \]

#### (c) Express the Bonus in Terms of B

The bonus is expressed as:

\[ 0.2B \]

#### (d) Express Gross Income in Terms of T and B

The gross income is also equal to the amount **T** on which taxes are based plus the bonus paid:

\[ 1.14 = T + 0.2B \]

#### (e) Solve the System of Equations

- From part (b): $ 1.14 = B + 0.2T $
- From part (d): $ 1.14 = T + 0.2B $

Solve these equations to find values for **T** and **B** (currently not filled).

#### (f) Determine Bonus and Taxes

- How much is the bonus?
- How much is paid in taxes?

This section requires solutions for the variables to determine the specific amounts for the bonus and taxes. The answer fields are currently blank.

**Educational Content: Calculating Financial Insights**

**Financial Calculations Interface**

1. **Bonus Calculation:**
- Query: "How much is the bonus?"
- Input Field: Enter the bonus amount in millions of dollars.

2. **Tax Calculation:**
- Query: "How much is paid in taxes?"
- Input Field: Enter the tax amount in millions of dollars.

3. **Profit Calculation:**
- Query: "How much profit is left over?"
- Input Field: Enter the remaining profit in millions of dollars.

Additionally, users can see:
- A labeled field for `T`, currently set at 1.14 with an error indicated by a red cross.
- An unlabeled field for `B`.

At the bottom, there is a help option available:
- Link/Button: "Need Help?" followed by a "Read It" button for additional guidance.

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