between 400 and 500.
ones digit is 2 less than the hundreds digit
tens digit is 2 less than the ones digit
The hundreds digit must be 4.
Take it from there.
between 100 and 200.
. tens digit is 3 less than the hundreds digit.
.ones digit is 1 more than the tens digit
To find the number between 400 and 500 that satisfies the given conditions, let's break down the conditions step by step.
1. The ones digit is 2 less than the hundreds digit.
Let's denote the ones digit as x and the hundreds digit as x + 2.
2. The tens digit is 2 less than the ones digit.
Let's denote the tens digit as x - 2.
Based on the given conditions, the number can be written in the form "hundreds digit + tens digit + ones digit." So the number is as follows:
Number = (x + 2) * 100 + (x - 2) * 10 + x
Considering that the number is between 400 and 500, let's substitute the limits into the equation and solve for x.
400 ≤ (x + 2) * 100 + (x - 2) * 10 + x ≤ 500
Simplifying this inequality, we get:
400 ≤ 111x ≤ 500
Dividing the inequality by 111, we have:
3.60 ≤ x ≤ 4.50
Since x represents a digit, it can only be a whole number. Therefore, the possible values for x are 4 and 5.
For x = 4:
Number = (4 + 2) * 100 + (4 - 2) * 10 + 4 = 642
For x = 5:
Number = (5 + 2) * 100 + (5 - 2) * 10 + 5 = 753
So, the numbers between 400 and 500 that satisfy the given conditions are 642 and 753.
To find the three-digit number that satisfies the given conditions, we can start by listing out the possible values for each digit and eliminating the ones that don't fit the criteria:
1. The hundreds digit can be any number between 4 and 5, inclusive: 4, 5.
2. The ones digit is 2 less than the hundreds digit. Since the ones digit is always less than the hundreds digit, we can eliminate the possibility of the ones digit being 4. Therefore, the ones digit can only be 5.
3. The tens digit is 2 less than the ones digit. Since the ones digit is 5, the tens digit can only be 3.
Combining the three digits, we get the number 435, which satisfies all the given conditions.