Question

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)
Responses

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

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

Answer 1

Let's break down the problem step by step.

1. **Understanding the Current Ages:**
- Let \( a \) be Tony’s current age.
- Since Andrea is 6 years younger than Tony, her current age can be expressed as \( a - 6 \).

2. **Ages in Two Years:**
- In two years, Tony’s age will be \( a + 2 \).
- In two years, Andrea’s age will be \( (a - 6) + 2 = a - 4 \).

3. **Setting Up the Equation:**
According to the problem, in two years, Tony's age will be three times Andrea's age. This can be formulated as:
\[
a + 2 = 3(a - 4)
\]

Now, let's identify which of the given equations can be used to find Andrea's and Tony's current ages.

- **Checking the options:**
1. \( a + 2 = 3(a - 6 + 2) \)
- This simplifies to \( a + 2 = 3(a - 4) \), which is our equation. **(Correct)**

2. \( a = 3(a + 2) \)
- This does not align with our problem statement. **(Incorrect)**

3. \( 3(a + 2) = a - 6 + 2 \)
- This simplifies to \( 3(a + 2) = a - 4 \), which is not correct. **(Incorrect)**

4. \( a + 2 = 3(a + 6 + 2) \)
- This simplifies to \( a + 2 = 3(a + 8) \), which is not correct. **(Incorrect)**

Thus, the correct equation to find Andrea's and Tony's current ages is:

**\( a + 2 = 3(a - 4) \)**, which is represented by option 1:
**\( a + 2 = 3(a - 6 + 2) \)**.