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)

Question

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 set up the equations based on the problem statement:

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

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, which gives us the equation:

\[ a + 2 = 3((a - 6) + 2) \]

This simplifies to:

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

Now let's look for the equation from the options provided. The only equation that matches our setup is:

a + 2 = 3(a − 6 + 2)

So the correct equation you can use to find Andrea's and Tony's current ages is:

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