Find 2 Numbers to fit all these rules:
1. To the nearest ten and hundred, both round to be the same number.
2. The estimated sum is 200.
3 The estimated difference is 0.
To find two numbers that satisfy all the given rules, let's break down the process step by step:
1. To the nearest ten and hundred, both round to be the same number:
This means that both numbers need to have the same digit in the tens and hundreds place. Let's assume the tens and hundreds place is 'x'. So, the numbers will be in the form 'x0x', where 'x' represents the unknown digit.
2. The estimated sum is 200:
If we assume the first number to be 'x0x', then the second number should be (at most) 'x' greater than the first number to get an estimated sum of 200. Therefore, the second number will be 'x0x + x', which can be simplified to 'x1x'.
3. The estimated difference is 0:
For the estimated difference to be 0, both numbers should be equal. So, we have 'x0x' = 'x1x'.
Now, let's solve for 'x':
By comparing the digits from the hundreds place, we get:
x = x
Due to the equal sign, we can ignore the 'x' completely, and it means that any digit will work for 'x' since it satisfies the equation.
Therefore, there are multiple solutions for 'x'. Here are a few examples:
- If 'x' is 1: The two numbers will be 101 and 111.
- If 'x' is 2: The two numbers will be 202 and 212.
- If 'x' is 3: The two numbers will be 303 and 313.
- And so on, for any digit 'x'.
In conclusion, there are infinitely many pairs of numbers that satisfy all the given rules.
Let's proceed step-by-step to find the two numbers that fulfill all the given rules.
Step 1: List all the possible numbers that round to the same number when rounded to the nearest ten and hundred:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, ...
Step 2: Consider the estimated sum is 200. From the list above, we can eliminate any numbers that are greater than 200, since the sum of the two numbers should equal 200.
Eliminated: 210, 220, 230, ....
Remaining: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200.
Step 3: Consider the estimated difference is 0. This means that the two numbers should be equal to each other. Therefore, we need to find two identical numbers from the remaining list.
Answer: The two numbers that satisfy all the given rules are 100 and 100.