Nancy said, In my number, the hundreds are one more than the tens, the tens are one more than the ones. The sum of the digits is 6. What number is Nancy thinking of

321

Solve

Let's solve this step by step.

Step 1: Let's call the hundreds digit "h," the tens digit "t," and the ones digit "o."

Step 2: According to Nancy, the hundreds digit is one more than the tens digit. So we can write this as h = t + 1.

Step 3: Similarly, the tens digit is one more than the ones digit. So we can write this as t = o + 1.

Step 4: The sum of the digits is 6. So we can write this as h + t + o = 6.

Step 5: Now let's substitute the values from steps 2 and 3 into step 4 to get a simplified equation: (t + 1) + t + (o + 1) = 6.

Step 6: Simplify the equation: 2t + o + 2 = 6.

Step 7: Rearrange the equation: 2t + o = 6 - 2.

Step 8: Further simplify: 2t + o = 4.

Step 9: Now, let's find all possible values for (t, o) that satisfy this equation.

- If t = 2, then 2*2 + o = 4, which gives us o = 0.
- If t = 1, then 2*1 + o = 4, which gives us o = 2.
- If t = 0, then 2*0 + o = 4, which has no valid solution.

Step 10: Based on the valid solutions from step 9, we have two possible sets of (h, t, o) values: (3, 2, 0) and (2, 1, 2).

Therefore, Nancy could be thinking of either the number 320 or the number 212.

To find the number Nancy is thinking of, let's start by assigning variables to each digit in the number.

Let's say the ones digit is 'x'.

According to Nancy's statement, the tens digit would be 'x + 1', since it's one more than the ones digit.

Similarly, the hundreds digit would be 'x + 1 + 1', since it's one more than the tens digit.

Now, let's form an equation using the given information. The sum of the digits is 6, so we can write:

x + (x + 1) + (x + 1 + 1) = 6

Simplifying the equation:

3x + 3 = 6

Subtracting 3 from both sides:

3x = 3

Dividing both sides by 3:

x = 1

Now that we have the value of 'x', we can substitute it back into our variable assignments:

The ones digit is 1, the tens digit is 1 + 1 = 2, and the hundreds digit is 2 + 1 + 1 = 4.

Therefore, the number Nancy is thinking of is 421.