Let's convert the given relationships into an equation.
Let's name the two number x and y.
The sum of the two numbers is 51: x + y = 51
One number is 15 more than the other: x = y + 15
Using the equations that we generated from the given relationships, let's determine the value of the two numbers by substitution.
Let's substitute x = y + 15 to x + y = 51.
[tex]\text{ x + y = 51 }\rightarrow\text{ (y + 15) + y = 51}[/tex][tex]\text{ y + 15 + y = 51 }\rightarrow\text{ 2y = 51 - 15}[/tex][tex]\text{ 2y = 36 }\rightarrow\text{ y = }\frac{36}{2}[/tex][tex]\text{ y = 18}[/tex]Since we now get the value of y, y = 18, let's determine the value of x.
[tex]\text{ x = y + 15 }\rightarrow\text{ x = 18 + 15}[/tex][tex]\text{ x = 33}[/tex]Therefore, the value of the two numbers is 18 and 33.