A residential property is assessed for tax purposes at 40% of its market value. The residential property tax is 3 1/3% of the assessed value and the tax is $1200.
a)What is the assessed value of the property?
b) What is the market value of the property?
1200 = 0.0333 * assessed value
assessed value = .4 * market value
solve the 1st equation for the assessed value, then plug this number into the second equation and solve for the market value
Thank youu!!!
To solve this problem, let's break it down step by step:
a) To find the assessed value of the property, we need to determine what value represents 100% of the market value. Since the assessed value is 40% of the market value, we can set up the following equation:
Assessed Value = 40% of Market Value
Let's represent the market value as "x" and solve for the assessed value:
Assessed Value = 0.40x
b) To find the market value of the property, we can use the fact that the property tax is 3 1/3% of the assessed value.
First, we need to find the assessed value based on the given property tax amount. Let's set up the equation:
Property Tax = 3 1/3% of Assessed Value
Given that the tax is $1200, we can convert 3 1/3% to its decimal form (0.0333):
$1200 = 0.0333 * Assessed Value
Now, let's substitute the value of the assessed value found in part a into the equation above:
$1200 = 0.0333 * (0.40x)
Now, we can solve the equation to find the market value (x).
To find the answers to these questions, we'll need to use some mathematical equations. Let's break down the problem step-by-step:
a) To find the assessed value of the property, we need to calculate 100% of the market value since the assessed value is 40% of the market value.
1. Let's assume the market value of the property is represented by "M."
2. Since the assessed value is 40% of the market value, we can calculate the assessed value using the equation: Assessed Value = 40% of M
3. To convert a percentage to a decimal, we divide it by 100. So, 40% can be expressed as 40/100 or 0.4.
4. Therefore, the equation to calculate the assessed value becomes: Assessed Value = 0.4 * M.
b) To find the market value of the property, we'll use the information that the residential property tax is 3 1/3% of the assessed value. We can calculate the market value using the following equation:
1. Let's assume the assessed value of the property is represented by "A."
2. Since the tax is 3 1/3% of the assessed value, we can calculate the tax using the equation: Tax = 3 1/3% of A.
3. To convert the mixed fraction 3 1/3 to a decimal, we can convert it to an improper fraction: 10/3. Then, divide 10 by 3, which equals 3.33 (rounded to the nearest two decimal places).
4. Therefore, the equation to calculate the tax becomes: Tax = 3.33/100 * A.
5. We know that the tax is $1200, so we can substitute Tax with $1200 and solve for A using the equation: $1200 = 3.33/100 * A.
By solving both equations, we can find the values of the assessed value (a) and the market value (b) of the property.