Let the original price of the coat is x. We know that there is 25% sale. We have been given that the price of coat after discount is $34.50.
We need to figure out the original price of coat, that is, the value of x.
We can set up an equation as shown below:
x - 25% of x = $34.50.
[tex]x-0.25x=34.50\\0.75x=34.50\\x=\frac{34.50}{0.75}=\$46[/tex]
Therefore, the original price of coat is 46 dollars.