Last year's salary was $38,600.
Work Step by Step
First, we need to define our unknown. What we want to find out is last year's salary, which we shall designate as $x$: This will be our unknown. We will need to add the amount of the salary increase to last year's salary to get this year's salary of $42,074$ dollars. Because the amount of the salary increase is $9$%, the amount of the increase can be given by the expression (9%)$(x)$. We cannot work directly 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. The percentage becomes $0.09$. We can now set up the following equation to find last year's salary: $$x + 0.09x = 42,074$$ We combine like terms: $$1.09x = 42,074$$ To solve for $x$, we divide both sides of the equation by $1.09$: $$x = 38,600$$ Last year's salary was $38,600.