Question

write two numbers that multiply to the value on top and add to the value on bottom.
24
×
□
+
□
11

Explanation:

Step1: Define variables and equations

Let the two numbers be \( x \) and \( y \). We have two equations: \( xy = 24 \) and \( x + y = 11 \).

Step2: Solve the system of equations

From \( x + y = 11 \), we can express \( y = 11 - x \). Substitute into \( xy = 24 \):
\( x(11 - x)=24 \)
\( 11x - x^{2}=24 \)
\( x^{2}-11x + 24 = 0 \)
We can also try factor pairs of 24. The factor pairs of 24 are (1,24), (2,12), (3,8), (4,6). Now check which pair adds up to 11.
\( 3 + 8 = 11 \) and \( 3\times8 = 24 \).

Answer:

3 and 8 (or 8 and 3)