To find the mystery number, we need to analyze the given information systematically and solve for each digit.
Let's start with the statement that the tens digit is the sum of the hundreds digit and the thousands digit. We can express this as an equation:
Tens digit = Hundreds digit + Thousands digit
Next, the problem states that the tens digit is twice the ones digit. We can write this as:
Tens digit = 2 * Ones digit
Moving on, the hundreds digit is said to be one more than zero, meaning it is equal to 1:
Hundreds digit = 1
Additionally, the thousands digit is defined as seven times the hundreds digit:
Thousands digit = 7 * Hundreds digit
Finally, the ten thousands digit is the same as the ones digit:
Ten thousands digit = Ones digit
Now, let's solve for each digit step by step:
From the given information, we know that:
- The hundreds digit = 1
- The thousands digit = 7 * 1 = 7
- The ten thousands digit = Ones digit
Using the equation Tens digit = Hundreds digit + Thousands digit, we can substitute the known values and rewrite it as:
Tens digit = 1 + 7 = 8
Using the equation Tens digit = 2 * Ones digit, we can substitute the known value for the tens digit and rewrite it as:
8 = 2 * Ones digit
To solve for the ones digit, we divide both sides of the equation by 2:
8 / 2 = Ones digit
Ones digit = 4
Therefore, from the given conditions, the mystery number is 87414.