Answer
$x + y = 81$
$y = x + 41$
One number is $20$; the other number is $61$.
Work Step by Step
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 $61$.
