a teen age boy wrote his own age after his father's from this new four place he subtracted the absolute value of the difference of their ages bto get 4289 the sum of their ages was
Since the son's age is between 13 and 19, the father must be 43, so that if the son's age is x,
4300 + x – (43 – x) = 4289, so 2x = 32 and x = 16. So the sum of their ages is 43 + 16 = 59.
To solve this problem, we need to break it down step-by-step.
Let's assume the father's age is represented by "F" and the teenage boy's age is represented by "T".
Step 1: "A teen age boy wrote his own age after his father's from this new four place."
From this statement, we can gather that the boy wrote his own age after his father's age. This means the four-digit number formed by the father's age followed by the boy's age would be:
1000F + T
Step 2: "He subtracted the absolute value of the difference of their ages to get 4289."
According to this statement, the boy subtracted the absolute value of the difference of their ages (|F - T|) from the four-digit number to get 4289. So, we can write the equation as:
(1000F + T) - |F - T| = 4289
Step 3: "The sum of their ages was..."
The sum of their ages can be calculated by adding the father's age and the teenage boy's age. So, the equation becomes:
F + T = ?
To find their ages, we need to solve the equation (1000F + T) - |F - T| = 4289 and then calculate the sum of their ages.
Unfortunately, without more information or additional equations, we cannot determine the sum of their ages or calculate their individual ages.
To solve this problem, let's break it down step by step:
Step 1: Understand the given information.
From the given information, we know that a teenage boy wrote his own age after his father's age. We are also told that when the teenage boy subtracted the absolute value of the difference of their ages from a new four-digit number, he obtained a result of 4289.
Step 2: Assign variables.
Let's assign variables to the unknown ages. Let's call the teenage boy's age "x" and the father's age "y".
Step 3: Set up equations.
Based on the given information, we can set up the following equations:
- "x" is the teenage boy's age.
- "y" is the father's age.
- The teenage boy wrote his own age after his father's age, so we can write x = y + 1.
- The teenage boy subtracted the absolute value of the difference of their ages from a four-digit number and got 4289, so we can write: 1000 - |x - y| = 4289.
Step 4: Solve the equations.
Substituting x = y + 1 into the second equation, we get: 1000 - |(y + 1) - y| = 4289.
Simplifying further, we have: 1000 - |1| = 4289.
This simplifies to: 1000 - 1 = 4289.
Thus, 999 = 4289.
Step 5: Interpret the incorrect result.
From Step 4, we can see that the derived equation is not valid because it leads to an incorrect result. Therefore, there may be an error or inconsistency in the given information.
Based on the steps mentioned above, it appears that the given problem is not solvable with the current information provided.