document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190139>Question 1190139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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?<BR>\n" );
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document.write( "5% of 30,000 = 0.05*30000 = 1500<BR>\n" );
document.write( "If Betty's income was exactly $30,000, then she would pay $1500 in taxes\r<BR>\n" );
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document.write( "Since she paid more than $1500, this means her income is above $30,000.\r<BR>\n" );
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document.write( "Let x be the difference between the $30,000 mark and her taxable income.<BR>\n" );
document.write( "So her taxable income is 30,000+x dollars.\r<BR>\n" );
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document.write( "That extra amount of money earned (x) is taxed at a rate of 10%<BR>\n" );
document.write( "So she pays 0.10x dollars on top of the 1500 dollars taxed at the lower bracket.\r<BR>\n" );
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document.write( "The total tax bill is this expression<BR>\n" );
document.write( "1500 + 0.10x\r<BR>\n" );
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document.write( "Set it equal to $2100 and solve for x<BR>\n" );
document.write( "1500 + 0.10x = 2100<BR>\n" );
document.write( "0.10x = 2100-1500<BR>\n" );
document.write( "0.10x = 600<BR>\n" );
document.write( "x = 600/(0.10)<BR>\n" );
document.write( "x = 6000\r<BR>\n" );
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document.write( "We add that 6,000 onto the 30,000<BR>\n" );
document.write( "6,000+30,000 = 36,000\r<BR>\n" );
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document.write( "Her taxable income is $36,000 and she pays $2100 of it in taxes<BR>\n" );
document.write( "The effective tax rate is (2,100)/(36,000) = 0.0583 = 5.83% approximately\r<BR>\n" );
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document.write( "Answer: $36,000<BR>\n" );
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