Question

two numbers total 39 and have a difference of 19. find the two numbers. the larger number is , and the smaller number is

Explanation:

Step1: Set up equations

Let the larger number be $x$ and the smaller number be $y$. We have the system of equations: $x + y=39$ and $x - y = 19$.

Step2: Add the two equations

Adding the two - equations $(x + y)+(x - y)=39 + 19$. Simplifying the left - hand side gives $2x$, and the right - hand side gives $58$. So, $2x=58$.

Step3: Solve for $x$

Dividing both sides of $2x = 58$ by 2, we get $x=\frac{58}{2}=29$.

Step4: Solve for $y$

Substitute $x = 29$ into the first equation $x + y=39$, so $29 + y=39$. Subtracting 29 from both sides gives $y=39 - 29=10$.

Answer:

The larger number is 29, and the smaller number is 10.