If the sum of two numbers is 20 and their product is 96, what are the numbers? (

If the sum of two numbers is 20 and their product is 96, what are the numbers? (2021)

If the sum of two numbers is 20 and their product is 96, what are the numbers? (2021)

Step 1: Let the two numbers be x and y.
Step 2: Write down the equations based on the problem: x + y = 20 and xy = 96.
Step 3: From the first equation (x + y = 20), we can express y in terms of x: y = 20 - x.
Step 4: Substitute y in the second equation (xy = 96) with the expression from Step 3: x(20 - x) = 96.
Step 5: Expand the equation: 20x - x^2 = 96.
Step 6: Rearrange the equation to form a standard quadratic equation: x^2 - 20x + 96 = 0.
Step 7: Factor the quadratic equation: (x - 12)(x - 8) = 0.
Step 8: Set each factor to zero: x - 12 = 0 or x - 8 = 0.
Step 9: Solve for x: x = 12 or x = 8.
Step 10: Use the values of x to find y: If x = 12, then y = 20 - 12 = 8. If x = 8, then y = 20 - 8 = 12.
Step 11: The two numbers are 12 and 8.

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