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Mathematics - Algebraic Number Theory

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?

I've come up with 2 solutions and not sure which one is correct please help..

a) Simplify the expression.
4220 + .25x - .25*30650
4220+.25x - 7226.5
.25x + -3442.5

a) 4220 + 0.25(x - 30,650)
4220 + (.25x - .25(30,650))
4200 + (.25x - 7,662.50)

b)4220+ 40000/4 - 30650/4
4220+10000-7662.5
4220 + (2,337.5) = $6,557.50

c) THIS IS THE ONE GIVING ME THE PROBLEM I'M GETTING TO SOLUTIONS..
8440 + 8000/4-61300/4
8440 + 2000 - 15325
13115
2*6557.5 = 13115

They pay the same, $13,115
4220 + (.25(80,000) - 7,662.5)
4220 + (20,000 - 7,662.5)
4220+ (12337.5) = $16,557.5

Solution Preview

(a) Tax = 4220 + 0.25(x - 30650)

= 4220 + 0.25x - 0.25 * 30650

= 0.25x - 3442.50

(b) Tax = ...

Solution Summary

A Complete, Neat and Step-by-step Solution is provided.

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