Question

James and Thomas have a total of 25 years. David is 10 years older than James. How old is Thomas if 6 years from now, David will be 19 years old?

Answer 1

Hint:
Here, we will assume the age of James and David to be some variable. Then we will form two linear equations using the given information. We will simplify these equations using substitution to get the values of the variable. Then we will use these values to find the age of Thomas.

Complete step by step solution:
Let the age of James be $x$ years old.
It is given that James and Thomas have a total of 25 years hence, the age of Thomas will be $\left( {25 - x} \right)$ years old.
Also, let the age of David be $y$ years old.
Now, it is given that David is 10 years older than James.
Hence, if we subtract the age of James from the age of David, we will get the difference as 10 years.
Thus, we can write this mathematically as:
$y - x = 10$……………………………$\left( 1 \right)$
Now, 6 years from now,
Ages of the three boys will be 6 years more than that of their present age respectively.
Now, it is given that 6 years from now, David will be 19 years old but David’s present age is $y$ years.
So, after 6 years, he should be $\left( {y + 6} \right)$ years old.
Thus, equating these two, we get,
$y + 6 = 19$
Subtracting 6 from both the sides, we get,
$y = 13$
Hence, the present age of David is 13 years old.
Now, substituting $y = 13$ in equation $\left( 1 \right)$, we get,
$13 - x = 10$
$ \Rightarrow x = 3$
Therefore, the required present age of Thomas $ = \left( {25 - x} \right) = \left( {25 - 3} \right) = 22$ years

Hence, presently, Thomas is 22 years old.
This is the required answer.

Note:
To answer this question we should know how to represent given information, mathematically. Also, understanding the meaning of the question plays an important role in such types of questions because if for example, we understood the meaning incorrectly then we could write the equation as $x - y = 25$ or even find the age of James instead of Thomas, hence, making our answer completely wrong.