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

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

Options:

Correct Answer: 10

Exam Year: 2020

Solution:

Let the two numbers be x and y. We have x + y = 15 and xy = 50. Solving these equations gives the larger number as 10.

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.

Simultaneous Equations – The question tests the ability to solve a system of equations involving addition and multiplication.
Quadratic Equations – The product and sum of the numbers can be used to form a quadratic equation.