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?

Answer 1

Let's denote Andrea's current age as \( a - 6 \) (since Andrea is 6 years younger than Tony who is \( a \) years old).

In two years, Tony's age will be \( a + 2 \) and 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. We can set up the equation based on this information:

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

Now let's simplify and solve the equation:

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

2. Rearrange the equation to get all terms involving \( a \) on one side: \[ 2 + 12 = 3a - a \] \[ 14 = 2a \]

3. Divide by 2: \[ a = 7 \]

So one valid equation that can be used to find Andrea’s and Tony’s current ages is:

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