Seb's salary is $$ \$ X $$ per year. The tax system is such that Seb pays a $$ 15 \% $$ flat rate of income tax on his salary. The tax system is due for reform, and politicians have suggested the following: 1. Any income under $$ \$ 12,000 $$ should be tax free. 2. Anything above $$ \$ 12,000 $$ should be taxed at $$ 25 \% $$. Given that Seb will be paying $$ \$ 1,500 $$ more under the new system, calculate $$ X $$. You can assume that $$ X\$ 12,000 $$. Round your answer to the nearest dollar.

Question

Seb's salary is $$ \$ X $$ per year. The tax system is such that Seb pays a $$ 15 \% $$ flat rate of income tax on his salary. The tax system is due for reform, and politicians have suggested the following: 1. Any income under $$ \$ 12,000 $$ should be tax free. 2. Anything above $$ \$ 12,000 $$ should be taxed at $$ 25 \% $$. Given that Seb will be paying $$ \$ 1,500 $$ more under the new system, calculate $$ X $$. You can assume that $$ X>\$ 12,000 $$. Round your answer to the nearest dollar.

UpStudy AI · Accepted Answer

Let Seb's salary be $$ X $$ dollars. Under the current tax system, he pays a flat rate of $$ 15\% $$ on his entire income, so his tax is

$$
0.15X.
$$

Under the new tax system, the first $$ \$12,000 $$ is tax free, and the remaining $$ X - 12,000 $$ is taxed at $$ 25\% $$. Thus, his new tax is

$$
0.25 (X - 12,000).
$$

We are given that under the new system, Seb pays $$ \$1,500 $$ more in tax, so we have the equation

$$
0.25 (X - 12,000) = 0.15X + 1,500.
$$

Now, solve for $$ X $$:

1. Expand the left side:

$$
0.25X - 0.25 \times 12,000 = 0.25X - 3,000.
$$

2. Substitute back into the equation:

$$
0.25X - 3,000 = 0.15X + 1,500.
$$

3. Subtract $$ 0.15X $$ from both sides:

$$
0.25X - 0.15X - 3,000 = 1,500,
$$
$$
0.10X - 3,000 = 1,500.
$$

4. Add $$ 3,000 $$ to both sides:

$$
0.10X = 4,500.
$$

5. Divide both sides by $$ 0.10 $$:

$$
X = \frac{4,500}{0.10} = 45,000.
$$

Thus, Seb's salary is $$ \$45,000 $$.
Seb's salary is \$45,000.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Current System Tax Calculation:

New System Tax Calculation:

Setting Up the Equation:

Simplifying the Equation:

Solving for :

Conclusion:

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