Introductory Algebra for College Students (7th Edition)

$x + y = 62$ $y = x + 12$ One number is $25$; the other number is $37$.
If the sum of two numbers is $62$, then let us set the first number as $x$ and the second number as $y$. If we add them together, we should get $62$. Let us write an equation reflecting these details: $$x + y = 62$$ Let us set the second equation as $y$ being the larger number. We know that the larger number is $12$ more than the other number, so we have: $$y = x + 12$$ We can use the substitution method to substitute this expression in for $y$ in the first equation: $$x + (x + 12) = 62$$ Group like terms: $$(x + x) + 12 = 62$$ Combine like terms: $$2x + 12 = 62$$ Isolate the $x$ term by subtracting $12$ from both sides of the equation: $$2x = 50$$ Divide both sides by $2$ to solve for $x$: $$x = 25$$ Now that we have a value for $x$, we can plug this value into the second equation to come up with the value for $y$: $$y = 25 + 12$$ $$y = 37$$ One number is $25$; the other number is $37$.