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\(For 2021, the amount of U.S. federal tax owed T is a function of taxable income d: \[T(d) = \begin{cases} 0.1d & \text{if}~d \le 9875, \\ 0.12(d-9875) + 987.5 & \text{if}~ 9876 \le d \le 40125, \\ 0.22(d-40125) + 4617.5 & \text{if}~ 40126 \le d \le 85525, \\ 0.24(d-85525) + 14605.5 & \text{if}~ 85526 \le d \le 163300, \\ 0.32(d-163300) + 33271.5 & \text{if}~ 163301 \le d \le 207350, \\ 0.35(d-207350) + 47367.5 & \text{if}~ 207351 \le d \le 518400, \\ 0.37(d-518400) + 156235 & \text{if}~ d > 518400. \end{cases}\] Noam has 90000 in taxable income, and Betty has $120000. How much more tax does Betty pay?\)

 May 14, 2023
 #1
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7200

 May 14, 2023
 #2
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ty so much!smiley

Guest May 14, 2023
 #3
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Betty's 120,000 falls into the 85,526 < d < 163,300 bracket  

 

So her tax is figured as  

                                                              0.24(120,000 – 85,525) + 14,605.5  

From there it's  

just arithmetic ....  

                                                              0.24(34,475) + 14,605.5  

 

                                                              8,274 + 14,605.5  

Betty's tax, in dollars, is  

                                                              22,879.50 dollars   

.

 May 14, 2023

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