Question

A house has increased in value by 38% since it was purchased. If the current value is $345,000, what was the value when it was purchased?

Answer 1

Explanation

The formula for calculating the percent change over time is:

$\begin{gathered} p=\frac{N-O}{O}\cdot100 \\ \text{ Where} \\ p\text{ is the percent change } \\ N\text{ is the new value } \\ O\text{ is the old value} \end{gathered}$

In this case, we have:

$\begin{gathered} p=38 \\ N=345000 \\ O=x \end{gathered}$$\begin{gathered} p=\frac{N-O}{O}\cdot100 \\ 38=\frac{345000-x}{x}\cdot100 \\ \text{ Multiply by x from both sides} \\ 38x=x\cdot\frac{345000-x}{x}\cdot100 \\ 38x=(345000-x)100 \\ \text{ Divide by 100 from both sides} \\ \frac{38x}{100}=\frac{(345000-x)100}{100} \\ 0.38x=345000-x \\ \text{ Add x from both sides} \\ 0.38x+x=345000-x+x \\ 1.38x=345000 \\ \text{ Divide by 1.38 from both sides} \\ \frac{1.38x}{1.38}=\frac{345000}{1.38} \\ x=250000 \end{gathered}$Answer

The value of the house when purchased is 250,000.