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

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

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

Let's break down the problem step by step.

1. Understanding the Current Ages:

   • Let \( a \) be Tony’s current age.
   • Since Andrea is 6 years younger than Tony, her current age can be expressed as \( a - 6 \).

2. Ages in Two Years:

   • In two years, Tony’s age will be \( a + 2 \).
   • In two years, Andrea’s age will be \( (a - 6) + 2 = a - 4 \).

3. Setting Up the Equation: According to the problem, in two years, Tony's age will be three times Andrea's age. This can be formulated as: \[ a + 2 = 3(a - 4) \]

Now, let's identify which of the given equations can be used to find Andrea's and Tony's current ages.

• Checking the options:

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

     • This simplifies to \( a + 2 = 3(a - 4) \), which is our equation. (Correct)

  2. \( a = 3(a + 2) \)

     • This does not align with our problem statement. (Incorrect)

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

     • This simplifies to \( 3(a + 2) = a - 4 \), which is not correct. (Incorrect)

  4. \( a + 2 = 3(a + 6 + 2) \)

     • This simplifies to \( a + 2 = 3(a + 8) \), which is not correct. (Incorrect)

Thus, the correct equation to find Andrea's and Tony's current ages is:

\( a + 2 = 3(a - 4) \), which is represented by option 1:
\( a + 2 = 3(a - 6 + 2) \).