Final answer:
Tommy was 24 years old in 2010. To determine this, an equation representing his age as 4/5ths of what it would be in 6 years was set up and solved using algebra.
Step-by-step explanation:
The question asks us to determine Tommy's age in 2010 based on the information that in 2010 he was 4/5ths as old as he will be 6 years later. To solve this problem, we can use algebra. Let's define T as Tommy's age in 2010. In 6 years, Tommy will be T + 6 years old. According to the question, T is 4/5ths of T + 6. This gives us the equation:
\( T = \frac{4}{5}(T + 6) \)
To solve the equation, we first distribute the 4/5:
\( T = 4/5 \times T + 4/5 \times 6 \)
So,
\( T = 4/5 \times T + \frac{24}{5} \)
To isolate T, we'll move all the T terms to one side by subtracting 4/5 T from both sides:
\( \frac{1}{5}T = \frac{24}{5} \)
Now, multiply both sides by 5 to solve for T:
\( T = 24 \)
Thus, Tommy was 24 years old in 2010.