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The difference between two numbers is 7. This product is 144. Find the smaller number.

User Cascadox
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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.

User Robert Kolner
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