Problem Statement:
The product of two numbers is 10625. If one number is 17 times the other number, find the numbers.

Solution:

To solve this problem, we can use the concept of equations and substitution.

Step 1: Define the variables:
Let's assume that one number is x and the other number is y.

Step 2: Translate the given information into equations:
From the problem statement, we know that the product of the two numbers is 10625. Therefore, we can write the equation as:
x * y = 10625 ---(Equation 1)

We are also given that one number is 17 times the other number. Mathematically, this can be represented as:
x = 17y ---(Equation 2)

Step 3: Substitute the value of x from Equation 2 into Equation 1:
Substituting the value of x from Equation 2 into Equation 1, we get:
17y * y = 10625

Simplifying the equation, we have:
17y^2 = 10625

Step 4: Solve the equation:
To solve the equation, we need to isolate y. Dividing both sides of the equation by 17, we get:
y^2 = 625

Taking the square root of both sides, we have:
y = ±25

Step 5: Find the value of x:
Now that we have the value of y, we can substitute it back into Equation 2 to find the value of x:
x = 17 * 25 = 425

So, the two numbers are 425 and 25.

Summary:
The two numbers are 425 and 25. The number 425 is 17 times the number 25. The product of these two numbers is indeed 10625.