Question

1. Determine the taxable income, to the nearest penny, for an individual filing jointly who pays a tax of $546.37.

2. If an individual filing jointly pays a tax of $278.36, determine the taxable income. Express your answer to the nearest cent.

3. If an individual’s taxable income is $6,300 determine the amount of tax to the nearest cent.

142.50 + 0.05 (6,300 - 5,250) = $195

I think this is how you set up this problem but do not know how to set up numbers 1 and 2 because they are under $750 and 1% taxable income.

Please explain. Thank you!

Answer 1

The following table is from the Georgia Income Tax table for married persons filing jointly

Answer 2

@satellite73 @amistre64

Answer 3

i got no easy way to approach this.

maybe seeing what the limits on the taxes are for each group, then see where the 'taxes paid' fits in a group.

Answer 4

your number 3 is fine

Answer 5

I just started learning about this under the piecewise function chapter and I am really stuck on these how do I go about this?

Answer 6

[1%] + n% (income - min) = 546.37

its definantly a piecewise deal yeah

Answer 7

solving for income ...

546.37 - [1%]
------------ + min
n%

Answer 8

what are our equation pieces in this form?

Answer 9

what do you mean by equation pieces?

Answer 10

you have equations, that piece together a function ... hence the term - piecewise function

Answer 11

you know from #3 how to setup if you know income ...

solve it for taxes paid instead

Answer 12

would that be 0.01(x-750)?

Answer 13

[1%] + n% (income - min) = 546.37

solve for income ... i already did it for one of them

Answer 14

(546.37-7.50)/.02 + 750
(546.37-37.50)/.03 + 2250
(546.37-82.50)/.04 + 3750
(546.37-142.50)/.05 + 5250
(546.37-230.00)/.06 + 7000

Answer 15

if the results are greater than the min of the next piece, then you know you dont have the correct piece.

Answer 16

graphing it might be productive if you can

Answer 17

27,693.5
19,212.33
15,346.75
13,327.4
12,272.83

Answer 18

I did the same thing for number 2 except replaced the $546.37 with $278.36

14,293
10,278.66
8,646.5
7,967.2
7,806

Answer 19

that was NOT easy to type up lol

Answer 20

and i didnt define the pieces quit right ...

Answer 21

Thank you for taking the time to type that up :)

Answer 22

http://www.wolframalpha.com/input/?i=+plot [piecewise[{{.01x%2C0%3Cx%3C750}%2C{7.50%2B.02%28x-750%29%2C750%3Cx%3C2250}%2C{37.50%2B.03%28x-2250%29%2C2250%3Cx%3C3750}%2C{82.50%2B.04%28x-3750%29%2C3750%3Cx%3C5250}%2C{142.50%2B.05%28x-5250%29%2C5250%3Cx%3C7000}%2C{230%2B.06%28x-7000%29%2Cx%3E7000}}]%2C{x%2C0%2C13000}]

Answer 23

might have to copy past it all in the browser to get to the link

Answer 24

@amistre64 where do I go from there?

Answer 25

but as i suspected, its the highest taxbracket for number 1 .... y=547 crosses over there

Answer 26

do you see that they are both in the last tax bracket?

Answer 27

yeah

Answer 28

anything paid over 230 is going to be in the last tax pracket it seems

Answer 29

@amistre64 I am still not clear as to what the answer would be though?

Answer 30

@amistre64 does this apply to both of the problems?

Answer 31

in hindsight, it might be best just to define the range of each piece. if you have the time.

Answer 32

0 to .01(750)
7.50 to 7.5+.02(2250-750)
37.50 to 37.5+.03(3750-2250)
82.50 to 82.5+.04(5250-3750)
142.50 to 142.5+.05(7000-5250)
230 to (skies the limit)

then see where the taxes paid fits in to determine the rest

Answer 33

notice that 547 and 278 are both greater than 230 ... so they will be worked out in that piece of the function.

Answer 34

so do I continue what you just did and go from 230?

Answer 35

yeah I see that they are both greater that 230

Answer 36

what is giving you issue here?

Answer 37

my issue is understanding what is the tax is like I did in number 3 which was $195 very easy for me to figure out these other two problems I don't know why this is so complicated and can't come up with an answer.

Answer 38

you realize that the function is defined in pieces, a function of functions ...

each part has its own domain and range that it cares for.

you are given a range element in questions 1 and 2, and asked to find the domain that it comes from. the hardest part is locating which function relates to the stated range.

after than, you only have to focus on that one part.

Answer 39

the domain of a, relates the range for 1
the domain of b, relates the range for 2

etc ...

of the range given is in say part 3, then we focus on the function defined for a domain of c and a range of 3

Answer 40

it just so happens, that questions 1 and 2 here, both pertain to the highest tax bracket, since anything over 230 in taxes is paid out by the last function

230 + .06(income - 7000) = tax paid

we know the taxes paid, so we simply solve for income

Answer 41

1. 546.37=230+0.06(income−7000)
316.37=0.06(income−7000)
5272.83=income−7000

income=$12272.83

2. 278.36=142.50+0.05(income−5250)

income=$7967.20

I think I understand it now.

Answer 42

spose taxes paid we 114.76

which part would we use?