Introductory Algebra for College Students (7th Edition)

$x + y = 81$ $y = x + 41$ One number is $20$; the other number is $61$.
If the sum of two numbers is $81$, then let us set the first number as $x$ and the second number as $y$. If we add them together, we should get $81$. Let us write an equation reflecting these details: $$x + y = 81$$ Let us set the second equation as $y$ being the larger number. We know that the larger number is $41$ more than the other number, so we have: $$y = x + 41$$ We can use the substitution method to substitute this expression in for $y$ in the first equation: $$x + (x + 41) = 81$$ Group like terms: $$(x + x) + 41 = 81$$ Combine like terms: $$2x + 41 = 81$$ Isolate the $x$ term by subtracting $41$ from both sides of the equation: $$2x = 40$$ Divide both sides by $2$ to solve for $x$: $$x = 20$$ Now that we have a value for $x$, we can plug this value into the second equation to come up with the value for $y$: $$y = 20 + 41$$ $$y = 61$$ One number is $20$; the other number is $61$.