If the sum of two numbers is 12 and their product is 32, what are the two number

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Question: If the sum of two numbers is 12 and their product is 32, what are the two numbers?

Options:

Correct Answer: 4 and 8

Solution:

The numbers that satisfy both conditions are 4 and 8, as 4 + 8 = 12 and 4 * 8 = 32.

If the sum of two numbers is 12 and their product is 32, what are the two numbers?

If the sum of two numbers is 12 and their product is 32, what are the two numbers?

Step 1: Let the two numbers be x and y.
Step 2: Write down the first condition: x + y = 12.
Step 3: Write down the second condition: x * y = 32.
Step 4: From the first condition, express y in terms of x: y = 12 - x.
Step 5: Substitute y in the second condition: x * (12 - x) = 32.
Step 6: Expand the equation: 12x - x^2 = 32.
Step 7: Rearrange the equation to form a standard quadratic equation: x^2 - 12x + 32 = 0.
Step 8: Factor the quadratic equation: (x - 4)(x - 8) = 0.
Step 9: Solve for x: x = 4 or x = 8.
Step 10: Use the values of x to find y: If x = 4, then y = 12 - 4 = 8; If x = 8, then y = 12 - 8 = 4.
Step 11: The two numbers are 4 and 8.

Algebraic Equations – The problem involves solving a system of equations based on the sum and product of two numbers.
Quadratic Equations – The conditions can be transformed into a quadratic equation to find the roots representing the two numbers.