Final answer:
The problem posed is an algebraic one involving the sum and difference of two numbers. By setting up equations and substituting, the larger number is found to be 10 and the smaller number is 7.
Step-by-step explanation:
The student has posed a classic algebra problem: finding two numbers given their sum and their difference. To find the numbers, let's call the larger number x and the smaller number y. The problem states that the sum of two numbers is seventeen (x + y = 17) and one number is three less than the other (y = x - 3).
Substituting the second equation into the first, we get x + (x - 3) = 17. Simplifying this equation, we find 2x - 3 = 17. Adding 3 to both sides gives us 2x = 20, and dividing by 2 yields x = 10. Now, using the original second equation and our value for x, y = 10 - 3 = 7.
Therefore, the two numbers are 10 and 7.