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 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 plus 6 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

Answer 1

Let's break down the problem step by step.

1. Define the Variables:

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

2. Age 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 will be three times as old as Andrea: \[ a + 2 = 3(a - 4) \]

4. Choosing the Correct Equation:

   • Now we need to simplify the equation: \[ a + 2 = 3(a - 4) \] simplifies to: \[ a + 2 = 3a - 12 \] or rearranged: \[ 2 + 12 = 3a - a \implies 14 = 2a \implies a = 7 \]

Looking at the original expressions provided in the responses, the correct equation that matches our derived equation \( a + 2 = 3(a - 4) \) is:

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

This can be validated because \( a - 6 + 2 \) is equivalent to \( a - 4 \).

Thus, the equation that can be used to find Andrea's and Tony's current ages is: a + 2 = 3(a - 6 + 2)