Question

Two decimals numbers, to the thousandths, that have a sum of about 5 and a difference of about 3. Then do the math to prove it works.

Answer 1

Answer:

The numbers are approximately: 4.000 and 1.000

Step-by-step explanation:

The given parameters can be expressed as:

$\frac{x}{1000} + \frac{y}{1000} \approx 5$

$\frac{x}{1000} - \frac{y}{1000} \approx 3$

Required

Determine the numbers

In each of the equations, multiply by 1000

$1000 * [\frac{x}{1000} + \frac{y}{1000} \approx 5]$

$x + y \approx 5000$

$1000 * [\frac{x}{1000} - \frac{y}{1000} \approx 3]$

$x-y \approx 3000$

So, we have:

$x + y \approx 5000$

$x-y \approx 3000$

Add the two equations

$x + x + y - y \approx 5000 + 3000$

$2x \approx 8000$

Solve for x

$x \approx 8000/2$

$x \approx 4000$

Substitute $x \approx 4000$ in $x + y \approx 5000$

$4000 + y \approx 5000$

$y \approx 5000 - 4000$

$y \approx 1000$

Using:

$\frac{x}{1000} + \frac{y}{1000} \approx 5$

We have:

$\frac{4000}{1000} + \frac{1000}{1000} \approx 5$

$4.000 + 1.000 \approx5$

This implies that, the numbers approximates to 4.000 and 1.000, respectively.