Question

In 2008, the Social Security percentage was 6.2% for the first $102,000 earned. The Medicare percentage was 1.45% of your entire salary. Darby made $143,000 in 2008.
a. Write the combined taxes, y, as a piecewise function where x represents the income.

b. How much did Darby pay in Social Security tax?

c. How much did Darby pay in Medicare tax?

Answer 1

a. The combined taxes is represented by y and your total income is represented by x

Now, if the salary is greater than 102,000 social security is a fixed amount that is equal = 102,000*0.062 = 6,324. This is because you pay social security tax only on your first 102,000

The piece wise function is as follows:

y = 0.062*x +0.0145*x     if x <=102,000

y = 6,324 + 0.0145*x        if x>102,000

b. John's social security = 102,000*0.062 = $6,324 (Since you pay social security tax only on your first 102,000)

c. John's medicare  tax = 0.0145*102,000 = $1,479

Answer 2

Answer:

Let x be the income.

Let y be the combined taxes.

When $x$ then the income is less than maximum taxable income. Hence, we will pay social security tax on the whole income.

Social security tax = $0.062\times x=0.062x$

When $x\geq 102000$ then we will pay social security on the maximum taxable income.

Social security tax = $0.062\times102000=6324$ dollars

Hence, Darby paid $6324 in Social Security tax.

Medicare tax will be = $0.0145\times x=0.0145x$

So, Darby paid in medicare tax = $0.0145\times143000=2073.50$ dollars

Now combined tax or y = social security tax plus medicare tax

So, $y=0.062x+0.0145x=0.0765x$  when x<102000

and $y=6324+0.0145x$  when x≥102000