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

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

Options:

Correct Answer: 12 and 8

Solution:

The two numbers are 12 and 8, as they satisfy both the sum (12 + 8 = 20) and the product (12 * 8 = 96).

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

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

Step 1: Let the two numbers be x and y.
Step 2: Write down the equations based on the problem: x + y = 20 (for the sum) and x * y = 96 (for the product).
Step 3: From the first equation, express y in terms of x: y = 20 - x.
Step 4: Substitute y in the second equation: 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: Solve for x: x = 12 or x = 8.
Step 9: Find y using y = 20 - x: If x = 12, then y = 8; if x = 8, then y = 12.
Step 10: The two numbers are 12 and 8.

Algebraic Equations – The question tests the ability to set up and solve a system of equations based on given conditions (sum and product of two numbers).
Quadratic Equations – The problem can be transformed into a quadratic equation, testing the understanding of roots and factoring.