The person originally weighed $200$ pounds.
Work Step by Step
First, we need to define our unknown. What we want to find out is how much the person weighed originally, which we shall designate as $x$. We will need to subtract the amount of the weight loss from the original weight to get the final weight of $180$ pounds. The amount of the weight loss can be given by the expression (10%)$(x)$. We cannot work with percentages, so we change the percent into a decimal. We do this by dividing the percentage by $100$ to get rid of the percentage sign. We can now set up the following equation to find the original weight of this person: $$x - 0.10x = 180$$ We combine like terms: $$0.9x = 180$$ To solve for $x$, we divide both sides of the equation by $0.9$: $$x = 200$$ The person originally weighed $200$ pounds.