Question

A house has increased in value by 36% since it was purchased. If the current value is $578,000, what was the value when it was purchased?

Answer 1

The value when it was purchased was $425,000

Explanation:

The formula for calculating the percent change over time is:

`p = (N - O)/O*100` where `p` is the percent change, `N` is the New Value and `O` is the Old Value. In this problem we are given `p` (36) and the New Value ($578,000). We can substitute this into the formula and solve for `O`:

`36 = (578000 - O)/O * 100`

`36/100 = (578000 - O)/O * 100/100`

`36/100 = (578000 - O)/O`

`(36*O)/100 = O((578000 - O))/O`

`0.36*O = cancel(O)((578000 - O))/cancel(O)`

`0.36*O = 578000 - O`

`0.36*O + O = 578000 - O + O`

`1.36 O = 578000`

`(1.36 O)/1.36 = 578000/1.36`

`(cancel(1.36) O)/cancel(1.36) = 425000`

`O = 425000`