Bunuel wrote:
If the value of a piece of property decreases by 10 percent while the new tax rate on the property represents 110% of the original tax rate, what is the effect on the taxes?
(A) Taxes increase by 10 percent.
(B) Taxes increase by 1 percent.
(C) There is no change in taxes.
(D) Taxes decrease by 1 percent.
(E) Taxes decrease by 10 percent.
Multipliers and algebraLet (1)P = property's value
Let (1)T = tax
rateOriginal tax
amount=(property value)*(tax rate)
Original tax amount:
\(P*T = PT\)New tax
amount:(new property value)*(new tax rate)
New property value:
\(.90P\) (10 percent decrease)
New tax rate:
\(1.10T\) (10 percent increase)
New tax
amount:
\(.90P*1.1T =.99 PT\)Percent change:
\(\frac{New-Old}{Old} * 100\)
\(\frac{.99PT-1PT}{1PT}*100=\frac{-.01}{1}*100= -.01*100 =\) -1 percent (Minus sign = percent decrease)
Tax amount decreases by 1 percent
Answer D
Assign valuesIn this problem, "taxes" might be a subtle word for some people.
"Taxes" = tax amount, and
Tax amount = (Property value)*(tax rate)
Let original property value = $1,000
Let original tax rate = 10 percent = .10
Original "taxes" (tax amount):($1,000*.10) = $100
New property value = original decreased by 10% = 90% of original value
New property value: (.90 * $1,000) = $900
New tax rate, increased by 10 percent, = 110% of original tax rate:
New tax rate:
\(1.1(.10) = .11\)New tax amount:
\($900*(.11) = $99\)Percent increase or decrease in tax amount?
\(\frac{New-Old}{Old} * 100\)
\(\frac{$99-$100}{$100}*100= \frac{$-1}{$100}*100 = -.01*100=\)-1 percentTax amount decreases by 1 percent
Answer D
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