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

The numbers are approximately: 4.000 and 1.000

Explanation:

The given parameters can be expressed as:

`(x)/(1000) + (y)/(1000) \approx 5`

`(x)/(1000) - (y)/(1000) \approx 3`

Required

Determine the numbers

In each of the equations, multiply by 1000

`1000 * [(x)/(1000) + (y)/(1000) \approx 5]`

`x + y \approx 5000`

`1000 * [(x)/(1000) - (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:

`(x)/(1000) + (y)/(1000) \approx 5`

We have:

`(4000)/(1000) + (1000)/(1000) \approx 5`

`4.000 + 1.000 \approx5`

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