SOLUTION: 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 o

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.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if it varies directly, then y = k * x applies.
k is the constant of variation.
y can be the tax or the value of the house.
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.

assuming y is the value of the house, your initial equation becomes 90,000 = k * 1650.
solve for k to get:
k = 90,000 / 1650 = 15.54545455 rounded to 8 decimal places.
when the house is assessed at 426,000, the equation becomes:
426,000 = k * x
solve for x to get:
x = 426,000 / 15.54545455 = 7810.
that will be your solution.

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.
1650/90,000 = .018333333 rounded to 8 decimal places.
7810/426,000 = the same.
this confirms the solution is correct.

when y is the tax and x is the value of the house, y = k * x becomes 1650 = k * 90,000
solve for k to get:
k = 1650 / 90,000 = .1833333333 rounded to 10 decimal places.
when x = 426,000, the equation becomes:
y = .1833333333 * 426,000
solve for y to get:
y = 7810.

you get the same answer.
the value of k, however, is different, depending on whether y is the value of the house or y is the tax.

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