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.
100 and 100
200
To find two numbers that fit all these rules, we can use a systematic approach.
Let's start by considering the first rule: "To the nearest ten and hundred, both round to be the same number."
We can assume that the two numbers have the same last digit, as their rounded values to the nearest ten and hundred should be the same. Let's call this common last digit 'x'. So, the two numbers can be written as "ax" and "bx", where 'a' and 'b' represent the remaining digits.
Next, let's consider the second rule: "The estimated sum is 200."
To find the estimated sum, we can add the rounded values of the two numbers. The rounded values of "ax" and "bx" will be "a0" and "b0", respectively, as both numbers need to round to the same number when rounded to the nearest hundred. Therefore, we can write the equation as "a0 + b0 = 200."
Lastly, let's consider the third rule: "The estimated difference is 0."
To find the estimated difference, we can subtract the rounded values of the two numbers. In this case, both numbers need to round to the same number when rounded to the nearest ten. So, the rounded values of "ax" and "bx" will be "ax" and "bx", respectively. Therefore, we can write the equation as "ax - bx = 0."
Now, let's solve these equations to find the values of 'a', 'b', and 'x'.
From "a0 + b0 = 200", we can deduce that 'a' and 'b' must add up to equal 20. There are several possibilities for the values of 'a' and 'b' that would satisfy this condition. Let's consider one scenario where 'a = 10' and 'b = 10'.
From "ax - bx = 0", we can substitute 'a' and 'b' with 10: "10x - 10x = 0". Here, 'x' can be any digit, as long as it satisfies the condition that both numbers round to the same number when rounded to the nearest ten and hundred.
Hence, one set of numbers that fit all the given rules is "105" and "105" (where 'a = 10', 'b = 10', and 'x = 5').