This is a problem where the final result after increasing value by a percentage is given
We have to work with percentages and not with the values, that is why sometimes it's called inverse percentages
We need to know the value of the house before the increase of 24% was taken
If something is increased by 24%, then its value must be at 124%
That is because the original price is supposed to be 100%, and with the increase, now it will be 100% + 24% = 124%
We know the final price is $527,000 and we also know that price already has an increase of 24%, thus if P is the original price:
124%*P = 527,000
Recall that the % sign is replaced by a division over 100 to perform calculations:
124/100*P=527,000
Let's multiply by 100
124*P = 527,000 * 100
And divide by 124
P = 527,000 * 100 / 124 = 425,000
Thus, the original price of the house was $425,000
Let's check: Increase 425,000 by 24%:
425,000 * 24/100 = $102,000
Add to the original price:
$425,000 + $102,000 = $527,000
As specified in the question