Question

write two numbers that multiply to the value on top and add to the value on bottom.
50
×
+
15
answer attempt 4 out of 10
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Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( x \times y = 50 \) and \( x + y = 15 \).

Step2: Solve the system of equations

From \( x + y = 15 \), we can express \( y = 15 - x \). Substitute this into the multiplication equation: \( x(15 - x)=50 \).
Expand to get \( 15x - x^{2}=50 \), rearrange to \( x^{2}-15x + 50 = 0 \).
Factor the quadratic: \( x^{2}-15x + 50=(x - 5)(x - 10)=0 \).
So \( x = 5 \) or \( x = 10 \). If \( x = 5 \), then \( y = 10 \); if \( x = 10 \), then \( y = 5 \).

Answer:

The two numbers are 5 and 10 (or 10 and 5). So the boxes can be filled with 5 and 10 (in either order).