If the sum of two numbers is 15 and their product is 50, what is the larger numb

If the sum of two numbers is 15 and their product is 50, what is the larger number? (2020)

If the sum of two numbers is 15 and their product is 50, what is the larger number? (2020)

Step 1: Let the two numbers be x and y.
Step 2: Write down the equations based on the problem: x + y = 15 and xy = 50.
Step 3: From the first equation, express y in terms of x: y = 15 - x.
Step 4: Substitute y in the second equation: x(15 - x) = 50.
Step 5: Expand the equation: 15x - x^2 = 50.
Step 6: Rearrange the equation to form a standard quadratic equation: x^2 - 15x + 50 = 0.
Step 7: Use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = -15, c = 50.
Step 8: Calculate the discriminant: b² - 4ac = (-15)² - 4(1)(50) = 225 - 200 = 25.
Step 9: Find the square root of the discriminant: √25 = 5.
Step 10: Substitute back into the quadratic formula: x = (15 ± 5) / 2.
Step 11: Calculate the two possible values for x: x = (15 + 5) / 2 = 10 and x = (15 - 5) / 2 = 5.
Step 12: Identify the larger number: The larger number is 10.

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