Questions: During the last year the value of your house decreased by 30%. If the value of your house is 224,000 today, what was the value of your house last year? Round your answer to the nearest cent, if necessary.

During the last year the value of your house decreased by 30%. If the value of your house is 224,000 today, what was the value of your house last year? Round your answer to the nearest cent, if necessary.

Transcript text: During the last year the value of your house decreased by $30 \%$. If the value of your house is $\$ 224,000$ today, what was the value of your house last year? Round your answer to the nearest cent, if necessary.

Solution

Solution Steps

To find the value of the house last year, we need to determine the original value before the 30% decrease. We can set up an equation where the current value is 70% (100% - 30%) of the original value. Solving this equation will give us the original value.

Step 1: Define the Problem

We need to find the value of the house last year given that its value decreased by $30\%$ and its current value is $\$224,000$.

Step 2: Set Up the Equation

Let $V$ be the value of the house last year. The current value is $70\%$ of the original value because the house value decreased by $30\%$. Therefore, we can write the equation: \[ 0.70V = 224000 \]

Step 3: Solve for $V$

To find $V$, we divide both sides of the equation by $0.70$: \[ V = \frac{224000}{0.70} \]

Step 4: Calculate the Value

Perform the division to find $V$: \[ V = 320000 \]