Question 1190139: In city X, the first $30,000 of someone's annual income are taxed at the rate of 5%, while any income over $30,000 is taxed at the rate of 10%. If in a certain year Betty paid $2100 in city X taxes, what was her income that year?
Answer by math_tutor2020(3817)   (Show Source):
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5% of 30,000 = 0.05*30000 = 1500
If Betty's income was exactly $30,000, then she would pay $1500 in taxes
Since she paid more than $1500, this means her income is above $30,000.
Let x be the difference between the $30,000 mark and her taxable income.
So her taxable income is 30,000+x dollars.
That extra amount of money earned (x) is taxed at a rate of 10%
So she pays 0.10x dollars on top of the 1500 dollars taxed at the lower bracket.
The total tax bill is this expression
1500 + 0.10x
Set it equal to $2100 and solve for x
1500 + 0.10x = 2100
0.10x = 2100-1500
0.10x = 600
x = 600/(0.10)
x = 6000
We add that 6,000 onto the 30,000
6,000+30,000 = 36,000
Her taxable income is $36,000 and she pays $2100 of it in taxes
The effective tax rate is (2,100)/(36,000) = 0.0583 = 5.83% approximately
Answer: $36,000
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