Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)

Question

Responses

a+2=3(a+6+2)
a plus 2 equals 3 left parenthesis a plus 6 plus 2 right parenthesis

a+2=3(a−6+2)
a plus 2 equals 3 left parenthesis a minus 6 plus 2 right parenthesis

3(a+2)=a−6+2
3 left parenthesis a plus 2 right parenthesis equals a minus 6 plus 2

a=3(a+2)
a equals 3 left parenthesis a plus 2 right parenthesis

Answer 1

Let's break down the problem first:

1. Let \( a \) be Tony's current age.
2. Since Andrea is 6 years younger than Tony, her current age is \( a - 6 \).

In two years:

• Tony's age will be \( a + 2 \).
• Andrea's age will be \( (a - 6) + 2 = a - 4 \).

According to the problem, in two years, Tony will be three times as old as Andrea:

\[ a + 2 = 3(a - 4) \]

Now, let's simplify that:

\[ a + 2 = 3a - 12 \]

If we rearrange this to isolate terms, we get:

\[ 2 + 12 = 3a - a \]

\[ 14 = 2a \]

Thus, the correct equation that we derived is:

\[ a + 2 = 3(a - 4) \]

However, looking at the responses provided, the closest option to this formulation is not explicitly listed, but we can recheck the responses for their correctness:

1. \( a + 2 = 3(a + 6 + 2) \) → This is incorrect.
2. \( a + 2 = 3(a - 6 + 2) \) → This simplifies incorrectly to match conditions.
3. \( 3(a + 2) = a - 6 + 2 \) → This is also incorrect based on the logic of their ages in two years.
4. \( a = 3(a + 2) \) → This is not logically representative of their ages.

None of the provided responses match our derived equation accurately. However, it appears that the correct conclusion from the analysis should yield:

Correct Answer: None of the equations accurately reflect the derived relationship. If required to select the best approximation, revisit the context but none fits correctly as per the logic stated from the age problem.

Let me know if you need further assistance!