Question

If the sum of two numbers is 30 and their difference is 8. What is their product?

Answer 1

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

We are given the following two equations based on the problem statement:

1. \( x + y = 30 \)
2. \( x - y = 8 \)

To solve for \( x \) and \( y \), we can add the two equations together:

\[
(x + y) + (x - y) = 30 + 8
\]

This simplifies to:

\[
2x = 38
\]

Now, divide both sides by 2:

\[
x = 19
\]

Next, we can substitute \( x = 19 \) back into the first equation to find \( y \):

\[
19 + y = 30
\]

Subtracting 19 from both sides gives:

\[
y = 30 - 19 = 11
\]

Now that we have both numbers, \( x = 19 \) and \( y = 11 \), we can find their product:

\[
x \times y = 19 \times 11
\]

Calculating the product:

\[
19 \times 11 = 209
\]

Thus, the product of the two numbers is \( \boxed{209} \).