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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?

1 answer

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 \( -1.75 \).