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

Step-by-step explanation

The formula for calculating the percent change over time is:

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

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