The sum of my tens and hundreds digit is my thousands digit. My hundreds digit is 1 less than my tens digit. My ones digit is greater than 7 and a multiple of 4. My tens digit is is 3 less than my ones digit. What is my number?
ones ... >7 and 4n ... 8
tens ... 8 - 3 ... 5
hundreds ... 5 - 1 ... 4
thousands ... 5 + 4 ... 9
To solve this problem, we'll break it down and analyze the given information step by step.
Let's start by assigning variables to each of the digits in the number. We'll use the variables T (thousands digit), H (hundreds digit), Tn (tens digit), and O (ones digit).
Based on the given information, we can formulate the following equations:
Equation 1: T + H = Tn
This states that the sum of the tens and hundreds digit is equal to the thousands digit.
Equation 2: H = Tn - 1
This states that the hundreds digit is 1 less than the tens digit.
Equation 3: O > 7 and O is a multiple of 4.
This means that the ones digit is greater than 7 and a multiple of 4.
Equation 4: Tn = O - 3
This states that the tens digit is 3 less than the ones digit.
To find the number, we'll attempt to solve this system of equations step by step.
First, let's focus on Equation 4, which relates the tens digit (Tn) and the ones digit (O). Since O must be greater than 7 and a multiple of 4, the only possible values are 8 and 12. Since Tn = O - 3, the possible values for Tn are 8 - 3 = 5 or 12 - 3 = 9.
Next, we move to Equation 2, which relates the hundreds digit (H) to the tens digit (Tn). Since H = Tn - 1, we can substitute the possible values of Tn we found earlier. If Tn = 5, then H = 5 - 1 = 4. If Tn = 9, then H = 9 - 1 = 8.
Now, we have two possibilities for the hundreds digit: H = 4 or H = 8.
Moving on to Equation 1, which relates the sum of the tens and hundreds digit (Tn + H) to the thousands digit (T), we can substitute the possible values of H we found earlier.
If H = 4, then Tn + H = 5 + 4 = 9, which means T = 9.
If H = 8, then Tn + H = 9 + 8 = 17, which means T cannot be 17, as it exceeds the range of single-digit numbers.
Therefore, we conclude that T = 9, H = 4, Tn = 5, and O = 8.
Putting these digits together, the number is 9,458.