Problem Analysis
The task involves calculating the tax liability for each person based on their income using a progressive tax system. The formula provided is:
\[
\text{Tax Paid by Person X} = (\text{\$Income in this bracket} \times 0.15) + (\text{\$Income in this bracket} \times 0.30)
\]
This formula suggests that there are two brackets:
1.
15% Bracket: Income up to a certain threshold.
2.
30% Bracket: Income above the threshold.
From the examples:
- If a person earns
\$70,000/year, the calculation is:
\[
(\$50,000 \times 0.15) + (\$20,000 \times 0.30) = \$7,500 + \$6,000 = \$13,500
\]
This implies that the first
\$50,000 is taxed at
15%, and the remaining
\$20,000 is taxed at
30%.
- If a person earns
\$10,000/year, the calculation is:
\[
(\$10,000 \times 0.15) + (\$0 \times 0.30) = \$1,500 + \$0 = \$1,500
\]
This implies that all income up to
\$50,000 is taxed at
15%, and any income above
\$50,000 is taxed at
30%.
Step-by-Step Solution
#### Year 1 Tax Worksheet
We will calculate the tax for each person based on their income and the given formula.
1.
Amy: \$20,000
- All income (\$20,000) is taxed at 15%.
\[
\text{Tax Paid} = (\$20,000 \times 0.15) + (\$0 \times 0.30) = \$3,000 + \$0 = \$3,000
\]
2.
Betty: \$40,000
- All income (\$40,000) is taxed at 15%.
\[
\text{Tax Paid} = (\$40,000 \times 0.15) + (\$0 \times 0.30) = \$6,000 + \$0 = \$6,000
\]
3.
Charlie: \$60,000
- First \$50,000 is taxed at 15%, and the remaining \$10,000 is taxed at 30%.
\[
\text{Tax Paid} = (\$50,000 \times 0.15) + (\$10,000 \times 0.30) = \$7,500 + \$3,000 = \$10,500
\]
4.
Dimitry: \$80,000
- First \$50,000 is taxed at 15%, and the remaining \$30,000 is taxed at 30%.
\[
\text{Tax Paid} = (\$50,000 \times 0.15) + (\$30,000 \times 0.30) = \$7,500 + \$9,000 = \$16,500
\]
5.
Evelyn: \$100,000
- First \$50,000 is taxed at 15%, and the remaining \$50,000 is taxed at 30%.
\[
\text{Tax Paid} = (\$50,000 \times 0.15) + (\$50,000 \times 0.30) = \$7,500 + \$15,000 = \$22,500
\]
#### Total Tax Revenue for Year 1
Sum the total tax paid by all individuals:
\[
\text{Total Tax Revenue} = \$3,000 + \$6,000 + \$10,500 + \$16,500 + \$22,500 = \$58,500
\]
Filling in the Year 1 Tax Worksheet
| Person | Year 1 Income | Income taxed at 15% | Income taxed at 30% | Total Tax Paid |
|----------|---------------|---------------------|---------------------|----------------|
| Amy | \$20,000 | \$3,000 | \$0 | \$3,000 |
| Betty | \$40,000 | \$6,000 | \$0 | \$6,000 |
| Charlie | \$60,000 | \$7,500 | \$3,000 | \$10,500 |
| Dimitry | \$80,000 | \$7,500 | \$9,000 | \$16,500 |
| Evelyn | \$100,000 | \$7,500 | \$15,000 | \$22,500 |
|
Year 1 Total Tax Revenue |
\$58,500 |
Final Answer
\[
\boxed{\$58,500}
\]
Parent Tip: Review the logic above to help your child master the concept of discretion worksheet.
