Family paid $24,000 as a down payment for a home if this represents 12% of the price of the home, find the price of the home.
The Correct Answer and Explanation is:
To determine the price of the home, we can use the relationship between percentages, the total amount, and the portion of that amount. Specifically, if $24,000 represents 12% of the home’s price, the equation to find the total price is:
[
\text{Price of Home} = \frac{\text{Down Payment}}{\text{Percentage as Decimal}}
]
Here’s how to calculate:
- Convert the percentage to a decimal:
- ( 12\% = \frac{12}{100} = 0.12 )
- Substitute the known values into the equation:
[
\text{Price of Home} = \frac{24,000}{0.12}
] - Perform the division:
[
\text{Price of Home} = 200,000
]
Thus, the price of the home is $200,000.
Explanation (300 words):
The question involves calculating the total price of a home based on a partial payment (the down payment) and its percentage relative to the total. This is a fundamental percentage problem where we know the part (down payment) and the percentage it represents, and we need to find the total amount.
To solve this, the percentage must first be converted into a decimal. Percentages are fractions out of 100, so (12\%) is expressed as (0.12). Next, the formula (\text{Total} = \frac{\text{Part}}{\text{Percentage as Decimal}}) is used because dividing the known portion ((24,000)) by the percentage ((0.12)) gives the total amount.
The logic behind this is that the down payment represents one piece (12%) of the whole (100%). By dividing (24,000) by (0.12), you’re essentially calculating how many “12% portions” fit into the total price, which equals (200,000).
This calculation is often used in real estate to determine the overall cost of a property when the down payment percentage and value are provided. Knowing this helps potential buyers and real estate agents plan finances, as they can work backward to estimate property costs based on available budgets for a down payment.