The sum of two numbers is twenty-five. One number is five less than the other.

x=15, y=10

*Note: x and y are only variables used to solve this problem, but know that the two numbers are 15 and 10.

Step-by-step explanation:

For this problem, we can use system of equations. Let's use x for one number and y for the other.

First Equation:

x+y=25

We get this equation because it states that the sum of the two numbers is 25.

Second Equation:

y=x-5

We get this equation because it says one number (y) is 5 less than the other (x).

Since we have two equations, we can use substitution method to solve.

                                 [distribute 1 to (x-5)]

                                    [combine like terms]

                                        [add both sides by 5]

                                               [divide both sides by 2]

Now that we have x, we can plug it into any of the equations to find y.

                                         [plug in x=15]

                                        [subtract both sides by 15]

Finally, we have our answer, x=15 and y=10.