We are given the final value of the house after its price was increased by 24%
We must go back to the original price knowing the final price. It's called inverse percentage calculation
To calculate the 24% of the value, we multiply by 24 and divide by 100, that is
value * 24 / 100 = 0.24 * value
The original price of the house is 100%, the increase is 24%, thus the final value of the house is 100% + 24% = 124%
What we were given as data is 124% of the original price of the house
As we did above, to compute 124% of a value, we multiply by 124 and divide by 100. Being P the original price of the house, then the final value is
P * 124% = P * 124 / 100 = 1.24 * P
We know this value:
1.24 * P = $527,000
Divide by 1.24 both sides of the equation
P = $527,000 / 1.24 = $425,000
The original price of the house was $425,000
Let's check it out:
Original price: $425.000
Increase: 0.24 * 425,000 = $102,000
Final Price: $425,000 + $102,000 = $527,000
The condition is met and the question is answered