document.write( "Question 1165161: The property tax in a certain country varies directly as assessed valuation. If a tax of $1,650 is charged on a single-family home assessed at $90,000, determine the property tax on an apartment complex assessed at $426,000. \n" ); document.write( "
Algebra.Com's Answer #789671 by Theo(13342)\"\" \"About 
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if it varies directly, then y = k * x applies.
\n" ); document.write( "k is the constant of variation.
\n" ); document.write( "y can be the tax or the value of the house.
\n" ); document.write( "x will be the value of the house if y is the tax and x will be the tax when y is the value of the house.\r
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\n" ); document.write( "\n" ); document.write( "assuming y is the value of the house, your initial equation becomes 90,000 = k * 1650.
\n" ); document.write( "solve for k to get:
\n" ); document.write( "k = 90,000 / 1650 = 15.54545455 rounded to 8 decimal places.
\n" ); document.write( "when the house is assessed at 426,000, the equation becomes:
\n" ); document.write( "426,000 = k * x
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 426,000 / 15.54545455 = 7810.
\n" ); document.write( "that will be your solution.\r
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\n" ); document.write( "\n" ); document.write( "since the variation is direct, then the tax needs to be proportional, meaning the ratio between the tax and the value of the house needs to be the same.
\n" ); document.write( "1650/90,000 = .018333333 rounded to 8 decimal places.
\n" ); document.write( "7810/426,000 = the same.
\n" ); document.write( "this confirms the solution is correct.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "when y is the tax and x is the value of the house, y = k * x becomes 1650 = k * 90,000
\n" ); document.write( "solve for k to get:
\n" ); document.write( "k = 1650 / 90,000 = .1833333333 rounded to 10 decimal places.
\n" ); document.write( "when x = 426,000, the equation becomes:
\n" ); document.write( "y = .1833333333 * 426,000
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 7810.\r
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\n" ); document.write( "\n" ); document.write( "you get the same answer.
\n" ); document.write( "the value of k, however, is different, depending on whether y is the value of the house or y is the tax.\r
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