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

Answer 1

Let's break down the problem step by step.

1. Let \( a \) be Tony's current age.
2. Since Andrea is 6 years younger than Tony, we can express Andrea's age as \( a - 6 \).
3. In 2 years, Tony's age will be \( a + 2 \) and Andrea's age will be \( (a - 6) + 2 = a - 4 \).
4. According to the problem, in 2 years, Tony will be three times as old as Andrea, which gives us the equation:
\[
a + 2 = 3(a - 4)
\]

Now, let's check which of the options corresponds with the correct equation:

- **Option 1**: \( a + 2 = 3(a - 6 + 2) \)
- This simplifies to \( a + 2 = 3(a - 4) \) (which is correct).

- **Option 2**: \( a + 2 = 3(a + 6 + 2) \)
- This is incorrect. It suggests that Andrea is older than Tony.

- **Option 3**: \( 3(a + 2) = a - 6 + 2 \)
- This is incorrect because it doesn't represent the relationship properly.

- **Option 4**: \( a = 3(a + 2) \)
- This is incorrect because it does not accurately represent the age relationship.

The correct response is that the equation that can be used is:

**Option 1: \( a + 2 = 3(a - 6 + 2) \)**.