Final answer:
To find the numbers, set up a system of equations: x = 6y + 7 and x + y = 28. Solve the system by substituting the value of x in terms of y into the second equation and solving for y. Substitute the value of y back into the first equation to find x.
Step-by-step explanation:
To find the numbers, let's assign variables to represent the two numbers. Let's call one number 'x' and the other number 'y'. Based on the given information, we know that x is seven more than six times y, so we can write the equation: x = 6y + 7. We also know that the sum of the numbers is 28, so we can write the equation: x + y = 28. Now we can solve this system of equations to find the values of x and y.
Solving the system of equations:
Substitute the value of x from the first equation into the second equation: (6y + 7) + y = 28. Simplify the equation: 7y + 7 = 28. Subtract 7 from both sides: 7y = 21. Divide both sides by 7: y = 3. Substitute this value of y back into the first equation to find x: x = 6(3) + 7 = 25. Therefore, the numbers are x = 25 and y = 3.