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

Answer 1

To set up the equations for the ages of Tony and Andrea, let's define:

• \( a \): Tony's current age
• \( a - 6 \): Andrea's current age (since Andrea is 6 years younger than Tony)

In two years, Tony will be \( a + 2 \) years old, and Andrea will be \( (a - 6) + 2 = a - 4 \) years old.

According to the problem, in two years, Tony will be three times as old as Andrea. Therefore, we can write the equation:

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

Now let's simplify the equation:

1. Distribute the 3 on the right side: \[ a + 2 = 3a - 12 \]

2. Rearrange the equation to isolate \( a \): \[ 2 + 12 = 3a - a \] \[ 14 = 2a \] \[ a = 7 \]

So, Tony's current age \( a \) is 7, and Andrea's current age is \( a - 6 = 1 \).

Now, looking at the original options you provided, the correct choice corresponds to the simplification we made:

The equation that equals \( a + 2 = 3(a - 4) \) from the problem is: \[ a + 2 = 3(a - 6 + 2) \] (Which simplifies to \( a + 2 = 3(a - 4) \).)

So, the correct response is: a + 2 = 3(a - 6 + 2).