An improved residential property is valued at $150,000. If building value to land value ratios are typically 2 to 1, what would the land value indicated by allocation be?
A. $50,000
B. $75,000
C. $120,000
D. None of the above
Answer (2)
Define the variables: Let B be the building value and L be the land value.
Express the relationship: B = 2 L .
Set up the equation: B + L = 150 , 000 .
Solve for L : L = 3 150 , 000 = 50 , 000 . The land value is $50 , 000 .
Explanation
Problem Analysis We are given that the total value of an improved residential property is $150,000. The ratio of the building value to the land value is 2:1. We need to find the land value.
Expressing Building Value in Terms of Land Value Let's denote the building value as B and the land value as L . We know that the ratio of building value to land value is 2:1, so we can write this as: L B = 1 2 This implies that B = 2 L .
Setting up the Equation The total value of the property is the sum of the building value and the land value, which is given as 150 , 000. S o , w e ha v e : B + L = 150 , 000 N o w , s u b s t i t u t e B = 2L in t o t h ee q u a t i o n : 2 L + L = 150 , 000 3 L = 150 , 000 $
Solving for Land Value Now, we solve for L :
L = 3 150 , 000 L = 50 , 000 So, the land value is $50,000.
Final Answer The land value indicated by allocation is $50,000, which corresponds to option a.
Examples
Understanding property valuation is crucial in real estate. For instance, if you're planning to invest in a property, knowing the land value helps you assess the potential for future development or resale. If a property is valued at $200,000 and the building-to-land ratio is 3:1, the land value would be $50,000, calculated as $200,000 / (3+1). This knowledge aids in making informed investment decisions and understanding the market dynamics.
The land value indicated by allocation is $50,000, derived from the total property value of $150,000 and a building to land value ratio of 2 to 1. Therefore, option A is the correct choice.
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