Question

which two numbers when multiplied gives 40 but when added gives 13

Answer 1

Let's denote the two numbers as \( x \) and \( y \). According to your conditions:

1. \( x \cdot y = 40 \)
2. \( x + y = 13 \)

We can use these equations to solve for \( x \) and \( y \).

From the second equation, we can express \( y \) in terms of \( x \):
\[ y = 13 - x \]

Now we can substitute this expression for \( y \) into the first equation:
\[ x \cdot (13 - x) = 40 \]

Expanding that gives:
\[ 13x - x^2 = 40 \]

Rearranging this into standard quadratic form:
\[ x^2 - 13x + 40 = 0 \]

Now we can factor the quadratic:
\[ (x - 8)(x - 5) = 0 \]

Setting each factor to zero gives us the solutions:
1. \( x - 8 = 0 \) ⇒ \( x = 8 \)
2. \( x - 5 = 0 \) ⇒ \( x = 5 \)

Thus, the two numbers are \( 8 \) and \( 5 \).

Verifying:
- Their product: \( 8 \cdot 5 = 40 \)
- Their sum: \( 8 + 5 = 13 \)

So, the two numbers you are looking for are \( 8 \) and \( 5 \).