My thousands digit is twice my hundreds digit. The sum of my tens and ones digit is my thousands digit. My hundreds digit is 2 more than my tens digit. My tens digit is greater than 1 and less than 3. What 4 digit number am I?
8,426.
Let x represent the hundreds digit.
My thousands digit is twice my hundreds digit --> Thousands= 2X
Hundreds= X
My hundreds digit is 2 more than my tens digit. --> Tens= X-2
Ones= Y
The sum of my tens and ones digit is my thousands digit. --> 2X=(X-2)+Y
My tens digit is greater than 1 and less than 3--> Since it must be a whole number. 1<x<3, then x-2=2 so x=4
Plug in 4 for x to get the thousands, and tens. Then solve 2X=x-2+y to get the ones.
Answer is 8,426.
I am a 3 digit number greater than 500 my tens digit is double my ones digit and half my hundreds digit what number am i
Let's solve this step-by-step:
Step 1: Let's assume the thousands digit is x.
Step 2: According to the first condition, the thousands digit is twice the hundreds digit, so the hundreds digit would be x/2.
Step 3: According to the second condition, the sum of the tens and ones digit is equal to the thousands digit, so the tens and ones digit would be x.
Step 4: According to the third condition, the hundreds digit is 2 more than the tens digit, so x/2 = x + 2.
Step 5: Solving the equation from step 4, we get x/2 - x = 2, which simplifies to -x/2 = 2.
Step 6: Multiplying both sides of the equation by -2, we get x = -4.
However, the tens digit cannot be negative, so the initial assumption is incorrect.
Let's try another assumption:
Step 1: Let's assume the thousands digit is y.
Step 2: According to the first condition, the thousands digit is twice the hundreds digit, so the hundreds digit would be y/2.
Step 3: According to the second condition, the sum of the tens and ones digit is equal to the thousands digit, so the tens and ones digit would be y.
Step 4: According to the third condition, the hundreds digit is 2 more than the tens digit, so y/2 = y + 2.
Step 5: Solving the equation from step 4, we get y/2 - y = 2, which simplifies to -y/2 = 2.
Step 6: Multiplying both sides of the equation by -2, we get y = -4.
Again, the tens digit cannot be negative, so the second assumption is also incorrect.
Let's try one more assumption:
Step 1: Let's assume the thousands digit is z.
Step 2: According to the first condition, the thousands digit is twice the hundreds digit, so the hundreds digit would be z/2.
Step 3: According to the second condition, the sum of the tens and ones digit is equal to the thousands digit, so the tens and ones digit would be z.
Step 4: According to the third condition, the hundreds digit is 2 more than the tens digit, so z/2 = z - 2.
Step 5: Solving the equation from step 4, we get z/2 - z = -2, which simplifies to -z/2 = -2.
Step 6: Multiplying both sides of the equation by -2, we get z = 4.
So, if the thousands digit is 4, the hundreds digit would be 4/2 = 2, the tens and ones digit would be 4, and the number would be 4244.
Thus, the 4-digit number that satisfies all the given conditions is 4244.
To find the 4-digit number that satisfies the given conditions, we can break down the problem step by step.
Let's start by analyzing the information provided:
1. Thousands digit is twice the hundreds digit.
2. Sum of the tens and ones digit is equal to the thousands digit.
3. Hundreds digit is 2 more than the tens digit.
4. Tens digit is greater than 1 and less than 3.
Let's assign variables to each digit to help us solve the problem. We'll use the variables T (thousands), H (hundreds), Tn (tens), and O (ones) to represent the digits.
Based on condition 1, we know that T = 2H.
From condition 2, we have Tn + O = T.
Condition 3 states that H = Tn + 2.
Lastly, condition 4 tells us that 1 < Tn < 3.
Now, let's substitute the variables and solve for the digits:
From condition 1: T = 2H
We have H = Tn + 2 (from condition 3), so we can substitute this into the equation T = 2H:
T = 2(Tn + 2)
T = 2Tn + 4
Since the sum of Tn and O is equal to T (from condition 2), we have:
Tn + O = T
Substituting the value of T from the first equation:
Tn + O = 2Tn + 4
Rearranging the equation, we get:
O = Tn + 4
Now, let's consider the possible values for the tens digit, Tn:
Tn can be 2 or 3 (based on condition 4).
If Tn = 2:
O = 2 + 4
O = 6
If Tn = 3:
O = 3 + 4
O = 7
Since the sum of the tens and ones digit is equal to the thousands digit (from condition 2), we need to find values of T and H that satisfy this condition.
If Tn = 2, O = 6, and T = 2Tn + 4:
T = 2(2) + 4
T = 8
Since H = Tn + 2 and Tn = 2:
H = 2 + 2
H = 4
So, if Tn = 2, the number is 8246.
If Tn = 3, O = 7, and T = 2Tn + 4:
T = 2(3) + 4
T = 10
Since H = Tn + 2 and Tn = 3:
H = 3 + 2
H = 5
So, if Tn = 3, the number is 1057.
Therefore, the possible 4-digit numbers that satisfy the given conditions are 8246 and 1057.