Question

The distance on a number line between two numbers is 3 and a half . The sum of the two numbers is zero.
what are the two numbers?

Answer 1

Let's denote the two numbers as \( x \) and \( y \). According to the problem, we have two pieces of information:

1. The distance between the two numbers is \( 3.5 \):
\[
|x - y| = 3.5
\]

2. The sum of the two numbers is zero:
\[
x + y = 0
\]

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

Now, substitute \( y \) into the first equation:
\[
|x - (-x)| = 3.5
\]
This simplifies to:
\[
|x + x| = 3.5
\]
or
\[
|2x| = 3.5
\]

Now we can solve for \( x \):
1. If \( 2x = 3.5 \):
\[
x = \frac{3.5}{2} = 1.75
\]

2. If \( 2x = -3.5 \):
\[
x = \frac{-3.5}{2} = -1.75
\]

So, the possible values for \( x \) are \( 1.75 \) and \( -1.75 \).

Now, we find the corresponding values for \( y \):
1. If \( x = 1.75 \):
\[
y = -1.75
\]

2. If \( x = -1.75 \):
\[
y = 1.75
\]

Thus, the two numbers are \( 1.75 \) and \( -1.75 \).

In summary, the two numbers are \( 1.75 \) and \( -1.75 \).