write two numbers that when rounded to the greatest place value have an estimated sum of 11000 and an estimated difference of 3000, then find the exact sum and the exact difference and explain how you have reached your answers and why they will work.

An approximated value is used as an estimate of an actual value. Possible numbers that fit the given description are 6999.9 and 4000.2

Let the numbers be x and y. Such that:

Make x the subject

Substitute in

Collect like terms

Divide by 2

Recall that:

From the question, we understand that the numbers are not whole. i.e. the numbers are approximated.

So, we look for a number that can be approximated to 7000 and 4000.

Possible numbers are:

Please note that there are several other numbers that fit into the above description.

Using 6999.9 and 4000.2, the sum and difference are:

Read more about approximated values at:

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First, we have rounded numbers A and B, and we know that:

A + B = 11000

A - B = 3000

Now we can solve this system of equations by isolating one variable in one of the equations, i will choose A in the second equation:

A = 3000 + B.

Now we can replace this into the other equation:

3000 + B + B = 11000

2*B = 11000 - 3000 = 8000

B = 8000/2 = 4000

and:

A - 4000 = 3000

A = 3000 + 4000 = 7000.

But remember that our original numbers are not exactly whole numbers, they are rounded up, so we could write them as:

A = 6999.8 (that would be rounded up to 7000)

B = 3999.7 (that would be rounded up to 4000)

The sum is:

A + B = 10999.5 (notice that this would be rounded up to 11000)

A - B =  3000.1 (this would be rounded down to 3000)

If you want to learn more, you can read:

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