Question

The product of two factors is 24. The difference between the two is 10. What are the two factors?

Answer 1

Using a system of equations and factoring a quadratic equation, we determined that the two factors whose product is 24 and whose difference is 10 are 12 and 2.

Step-by-step explanation:

To find the two factors whose product is 24 and whose difference is 10, we can set up a system of equations based on the given information. Let's call the two factors x and y, where x is the larger factor.

1. x * y = 24 (Equation 1: the product of the two factors)
2. x - y = 10 (Equation 2: the difference between the two factors)

From Equation 2, we can express y as y = x - 10. Now we can substitute this expression into Equation 1:

x * (x - 10) = 24

Expanding the equation gives us:

x2 - 10x = 24

Moving all terms to one side gives us a quadratic equation:

x2 - 10x - 24 = 0

By factoring the quadratic equation, we find that the two solutions for x are 12 and -2. However, because we are looking for positive factors, we disregard -2 as a solution.

So, the larger factor x is 12. Using Equation 2, we can find the smaller factor y:

12 - y = 10

y = 2

Therefore, the two factors are 12 and 2.