124. Marriage penalty eliminated. The value of the expression
4220 + 0.25(x 30,650)
is the 2006 federal income tax for a single taxpayer with
taxable income of x dollars, where x is over $30,650 but
not over $74,200.
a) Simplify the expression.
b) Find the amount of tax for a single taxpayer with
taxable income of $40,000.
c) Who pays more, a married couple with a joint taxable
income of $80,000 or two single taxpayers with
taxable incomes of $40,000 each? See Exercise 123.
It looks like your formula is incorrect. Please repost with modified formula and more accurate data.
Thanks for asking.
a) To simplify the expression 4220 + 0.25(x - 30,650), we can start by distributing the 0.25 to the terms inside the parentheses. This gives us:
4220 + 0.25x - 0.25(30,650)
Next, we can simplify the expression -0.25(30,650) by multiplying -0.25 with 30,650:
4220 + 0.25x - 7662.5
Finally, we can combine like terms by adding 0.25x and -7662.5:
4220 + 0.25x - 7662.5 = 0.25x - 3442.5
So, the simplified expression is 0.25x - 3442.5.
b) To find the amount of tax for a single taxpayer with a taxable income of $40,000, substitute x = 40,000 into the simplified expression 0.25x - 3442.5:
0.25(40,000) - 3442.5 = 10000 - 3442.5 = 6557.5
Therefore, the amount of tax for a single taxpayer with a taxable income of $40,000 is $6,557.50.
c) To determine who pays more, we compare the tax amounts for a married couple with a joint taxable income of $80,000 and two single taxpayers with taxable incomes of $40,000 each.
For the married couple, we substitute x = 80,000 into the simplified expression 0.25x - 3442.5:
0.25(80,000) - 3442.5 = 20,000 - 3442.5 = 16557.5
So, the married couple will pay $16,557.50 in taxes.
For the two single taxpayers, we calculate the tax amount for each individual using the same process as in part b:
For the first single taxpayer with taxable income of $40,000:
0.25(40,000) - 3442.5 = 10000 - 3442.5 = 6557.5
And for the second single taxpayer with taxable income of $40,000:
0.25(40,000) - 3442.5 = 10000 - 3442.5 = 6557.5
The total tax amount for the two single taxpayers is 2 * 6557.5 = $13,115.
Comparing the amounts, the married couple pays more in taxes with $16,557.50 compared to the two single taxpayers who pay a total of $13,115.