Final answer:
To find two numbers with an estimated sum of 11,000 and an estimated difference of 3,000 when rounded to the greatest place value, set up a system of equations. By solving the equations, we determine that the numbers approximating to 7,000 and 4,000 after rounding meet the criteria. Example numbers could be 6,500 and 4,500 before rounding.
Step-by-step explanation:
We are looking for two numbers that, when rounded to the greatest place value, have an estimated sum of 11,000 and an estimated difference of 3,000. Let's call these two numbers X and Y. After rounding to the greatest place value, which is likely the thousands place for these numbers, their sum should be approximately 11,000 and their difference approximately 3,000.
Lets set up the system of equations:
- Estimated X + Estimated Y = 11,000
- Estimated X - Estimated Y = 3,000
Solving for these equations simultaneously, we can find the values of Estimated X and Estimated Y. Adding both equations we get:
- 2 * Estimated X = 14,000
- Estimated X = 7,000
Now substitute Estimated X in one of the equations to find Estimated Y:
- 7,000 + Estimated Y = 11,000
- Estimated Y = 11,000 - 7,000
- Estimated Y = 4,000
Thus, the two numbers that round to 7,000 and 4,000 could be something like 6,500 and 4,500 respectively. Their estimated sum is 11,000, and the estimated difference is 3,000 when rounded to the nearest thousand.