Write two numbers that multiply to the value on top and add to the value on bottom

Question

24

11

Answer 1

To find two numbers that multiply to 24 (the value on top) and add to 11 (the value on the bottom), we can set up the equations:

Let the two numbers be \( x \) and \( y \).

1. \( x \cdot y = 24 \)
2. \( x + y = 11 \)

We can solve for \( y \) in the second equation: \( y = 11 - x \)

Now, we can substitute \( y \) into the first equation:

\( x(11 - x) = 24 \)

Expanding this gives:

\( 11x - x^2 = 24 \)

Rearranging it leads to a quadratic equation:

\( x^2 - 11x + 24 = 0 \)

Now, we can factor the quadratic:

\( (x - 3)(x - 8) = 0 \)

So, the solutions for \( x \) are:

\( x = 3 \) or \( x = 8 \)

Thus, the two numbers are 3 and 8, since:

• \( 3 \cdot 8 = 24 \)
• \( 3 + 8 = 11 \)