Dennis wrote down a three digit number, The digit in the tens place is 2 more than the digit in the hundreds place. The digit in the ones place is 6less than the digit in the tens place. The digit in the hundreds place is odd number. What is the three digit number?
793 OR 571
t=digit in the tens place
the number is then
(t+2)t(t-6)
If (t+2) is odd, so is t.
t must be ≥ 6 or else t-6 is negative.
so t could be 7 or 9
But t cannot be greater than 7 (or else t+2 will have 2 digits)
therefore the three-digit number must be 571.
Let's solve this problem step-by-step:
Step 1: Start by setting up a system of equations based on the given information.
Let's assume the hundreds digit is represented by H, the tens digit is represented by T, and the ones digit is represented by O.
From the given information, we can write the following equations:
T = H + 2 (Equation 1)
O = T - 6 (Equation 2)
H is odd
Step 2: Use Equation 1 to find the value of T in terms of H.
Substitute H + 2 for T in Equation 2:
O = (H + 2) - 6
Simplifying:
O = H - 4 (Equation 3)
Step 3: Use Equation 3 to find the possible values of O.
Since the ones digit cannot be negative, we can set up the inequality:
0 ≤ H - 4
Solving for H:
H - 4 ≥ 0
H ≥ 4
So, the possible values for H are 4, 5, 6, 7, 8, and 9.
Step 4: Substitute the possible values of H into Equation 1 to find the corresponding values of T.
Using Equation 1:
T = H + 2
For H = 4, T = 4 + 2 = 6
For H = 5, T = 5 + 2 = 7
For H = 6, T = 6 + 2 = 8
For H = 7, T = 7 + 2 = 9
For H = 8, T = 8 + 2 = 10 (Not a valid digit)
For H = 9, T = 9 + 2 = 11 (Not a valid digit)
Step 5: Substitute the possible values of T into Equation 2 to find the corresponding values of O.
Using Equation 2:
O = T - 6
For T = 6, O = 6 - 6 = 0 (Not a valid digit)
For T = 7, O = 7 - 6 = 1
For T = 8, O = 8 - 6 = 2
For T = 9, O = 9 - 6 = 3
Step 6: Combine the possible values of H, T, and O to form three-digit numbers.
From the values obtained, we can form two three-digit numbers: 527 and 638.
Therefore, the two possible three-digit numbers that satisfy the given conditions are:
1. 527
2. 638
To find the three-digit number, we need to analyze the given information step by step.
Let's start by naming the digits in the hundreds, tens, and ones places as A, B, and C, respectively.
From the statement, we can conclude the following:
1. The digit in the tens place is 2 more than the digit in the hundreds place.
This can be written as: B = A + 2
2. The digit in the ones place is 6 less than the digit in the tens place.
This can be written as: C = B - 6
3. The digit in the hundreds place is an odd number.
This means that A is an odd number (1, 3, 5, 7, or 9).
Now, let's use these equations to find the values of A, B, and C:
From equation 1, we can substitute B in terms of A:
B = A + 2
Then, substitute B in equation 2:
C = (A + 2) - 6
C = A - 4
Now, let's analyze the possible values of A:
If A = 1, then C = 1 - 4 = -3 (which is not possible since C needs to be a digit).
If A = 3, then C = 3 - 4 = -1 (which is not possible since C needs to be a digit).
If A = 5, then C = 5 - 4 = 1.
And from equation 1, B = 5 + 2 = 7.
Therefore, our three-digit number is 571.
If A = 7, then C = 7 - 4 = 3.
And from equation 1, B = 7 + 2 = 9.
Therefore, our three-digit number is 793.
If A = 9, then C = 9 - 4 = 5.
And from equation 1, B = 9 + 2 = 11 (which is not possible since B needs to be a digit).
So, the two possible three-digit numbers that satisfy the given conditions are 571 and 793.