Final answer:
To find the smaller number when the difference between two numbers is 7 and their product is 144, set up an equation using x as the smaller number. Solve the quadratic equation to find that the smaller number is 9.
Step-by-step explanation:
To find the smaller number when the difference between two numbers is 7 and their product is 144, we can set up an equation. Let's call the smaller number x. The other number will be x + 7. We know that their product is 144, so we can write the equation as:
x * (x + 7) = 144
Expanding the equation, we get:
x^2 + 7x = 144
Next, rearrange the equation to form a quadratic equation:
x^2 + 7x - 144 = 0
Now we can solve this equation using factoring, completing the square, or the quadratic formula. After solving, we find that the smaller number is x = -16 or x = 9. Since we're looking for a positive number, the smaller number is 9.