i am a three digit number. my hundreds digit is three more than my ones digit.my tens digit is oneless than my hundreds digit. what numbers can i be?
Just start by putting 0, 1,2, ... into the ones digit
then fulfilling the other two conditions
320
431
542
653
764
875
986 , can't use 7 or higher for the unit digits
d = your digit
d = 100 x + 10 y + z
my hundreds digit is three more than my ones
x = z + 3
that is equivalent with :
z = x - 3
my tens digit is oneless than my hundreds
y = x - 1
d = 100 x + 10 y + z
d = 100 * x + 10 * ( x - 1 ) + x - 3
d = 100 x + 10 x - 10 + x - 3 = 111 x - 13
Solution 1 :
x = 9
y = x - 1 = 9 - 1 = 8
z = x - 3 = 9 - 3 = 6
d = 986
Solution 2 :
x = 8
y = x - 1 = 8 - 1 = 7
z = x - 3 = 8 - 3 = 5
d = 875
Solution 3 :
x = 7
y = x - 1 = 7 - 1 = 6
z = x - 3 = 7 - 3 = 4
d = 764
Solution 4 :
x = 6
y = x - 1 = 6 - 1 = 5
z = x - 3 = 6 - 3 = 3
d = 653
Solution 5 :
x = 5
y = x - 1 = 5 - 1 = 4
z = x - 3 = 5 - 3 = 2
d = 542
Solution 6 :
x = 4
y = x - 1 = 4 - 1 = 3
z = x - 3 = 4 - 3 = 1
d = 431
Solution 7 :
x = 3
y = x - 1 = 3 - 1 = 2
z = x - 3 = 3 - 3 = 0
d = 320
123
To solve this problem, let's break it down step by step:
1. Begin with the information given: the number is a three-digit number, and its hundreds digit is three more than its ones digit.
So, we can write the hundreds digit as (ones digit + 3).
2. The tens digit is one less than the hundreds digit.
Therefore, we can express the tens digit as (hundreds digit - 1).
3. Since we are dealing with a three-digit number, the possibilities for the hundreds, tens, and ones digits are limited to the range of 0 to 9.
4. Substitute the expressions we derived in step 1 and step 2:
- The hundreds digit = ones digit + 3.
- The tens digit = (ones digit + 3) - 1.
5. Simplify the equation:
- The tens digit = ones digit + 2.
6. We can now determine the possible values for each digit by substituting values from 0 to 9 into the equations:
For the ones digit, we can select any digit from 0 to 9.
For every value of the ones digit, we substitute it back into the equations to find the corresponding tens and hundreds digit.
Using a table to demonstrate:
| Ones Digit | Tens Digit | Hundreds Digit | Number |
|------------|------------|----------------|------------|
| 0 | 2 | 3 | 320 |
| 1 | 3 | 4 | 431 |
| 2 | 4 | 5 | 542 |
| 3 | 5 | 6 | 653 |
| 4 | 6 | 7 | 764 |
| 5 | 7 | 8 | 875 |
| 6 | 8 | 9 | 986 |
| 7 | 9 | 0 | 097 |
| 8 | 0 | 1 | 108 |
| 9 | 1 | 2 | 219 |
Therefore, the possible numbers that satisfy the given conditions are 320, 431, 542, 653, 764, 875, 986, 097, 108, and 219.