Question

Xavier is working as a lifeguard over the summer, for which he is paid $9 per hour. He did some research on federal income tax and determined that he must pay 10% of his income in federal income tax, 12.4% in Social Security tax, and 2.9% in Medicare tax. Write a linear function representing Xavier’s gross income (earnings before taxes) in terms of the number of hours (x) he works. Type your response here: Write a linear function representing the amount of money Xavier must pay in federal income tax in terms of the number of hours (x) he works. Type your response here: Write a linear function representing the amount of money Xavier must pay in Social Security tax in terms of the number of hours (x) he works. Type your response here: Write a linear function representing the amount of money Xavier must pay in Medicare tax in terms of the number of hours (x) he works. Type your response here: Write a linear function representing Xavier’s net income (earnings after taxes) in terms of the number of hours (x) he works. Type your response here: Look again at the simplest form of the linear function you created in part e for net income. What does the numerical value (the coefficient of x) mean in terms of Xavier’s situation? Type your response here: What will Xavier’s gross and net income be if he works 110 hours in a month? Type your response here: What will the difference of his gross income and net income be for 110 hours of work? Type your response here: What does the value you found in part h represent in terms of Xavier’s situation? Type your response here:

Answer 1

$9 ⇒ one hour
$9 × 2 ⇒ two hours
$9 × 3 ⇒ three hours
$9 × x ⇒ 'x' hours

Xavier's gross income = 9x
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Federal income tax = 10% of gross income
Federal income tax = 10% of 9x

10% as decimal is 0.1
Federal income tax = 0.1(9x)
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Medicare tax = 2.9% of gross income
Medicare tax = 2.9% of 9x

2.9% as decimal is 2.9÷100 = 0.029
Medicare tax = 0.029(9x)
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Social security tax = 12.4% of gross income
Social security tax = 12.4% of 9x

12.4% as decimal is 12.4÷100 = 0.124
Social security tax is = 0.124(0.9x)
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Net income = gross income - total tax
Net income = 9x - [0.1(0.9x) + 0.029(0.9x) + (0.124(0.9x)]
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The coefficient of x in Xavier's equation is for 'the number of hours worked'

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Xavier's gross income when x = 110 is 9×110 = $990

Total taxes that Xavier needs to pay is:
Federal tax + Social security tax + Medicare tax
[0.1 × 9x] + [0.124 × 9x] + [0.029 × 9x]
[0.1 × 990] + [0.124 × 990] + [0.029 × 990]
99+122.76+28.71 = 250.47

Net income = gross income - total tax
Net income = 990 - 250.47 = $739.53
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Difference between net income and gross income

990 - 739.53 = 250.47
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Xavier net income of $250.47 is the amount he received after taxes.