Question

write two numbers that multiply to the value on top and add to the value on bottom.
40
×

+
13
answer
attempt 1 out of 10

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( x \times y = 40 \) and \( x + y = 13 \).

Step2: Solve the system of equations

From \( x + y = 13 \), we can express \( y = 13 - x \). Substitute this into the multiplication equation: \( x(13 - x)=40 \).
Expand to get \( 13x - x^{2}=40 \), rearrange to \( x^{2}-13x + 40 = 0 \).
Factor the quadratic equation: \( x^{2}-13x + 40=(x - 5)(x - 8)=0 \).
So \( x = 5 \) or \( x = 8 \). If \( x = 5 \), then \( y = 13 - 5 = 8 \); if \( x = 8 \), then \( y = 13 - 8 = 5 \).

Answer:

5 and 8 (or 8 and 5)