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

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)
a plus 2 equals 3 left parenthesis a plus 6 plus 2 right parenthesis

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

a+2=3(a−6+2)

Answer 1

To solve the problem, let's define the variables:

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

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's age will be three times Andrea's age. This gives us the equation:

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

Now let's examine the provided options to find which one matches our derived equation:

1. \( 3(a + 2) = a - 6 + 2 \) simplifies to \( 3a + 6 = a - 4 \) (Not correct).
2. \( a + 2 = 3(a + 6 + 2) \) does not match our equation (Not correct).
3. \( a = 3(a + 2) \) simplifies to \( a = 3a + 6 \) (Not correct).
4. \( a + 2 = 3(a - 6 + 2) \) simplifies to \( a + 2 = 3(a - 4) \), which matches our derived equation.

Therefore, the correct option is:

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