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 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) a plus 2 equals 3 left parenthesis a minus 6 plus 2 right parenthesis

Answer 1

To find the correct linear equation, we can break down the information provided.

Let:

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

In two years:

• Tony's age will be \( a + 2 \).
• 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. This gives us the equation:

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

Now we can simplify this equation:

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

2. Rearrange it to isolate terms involving \( a \): \[ 2 + 12 = 3a - a \] \[ 14 = 2a \] \[ a = 7 \]

To find the linear equation from the options given that corresponds to our derived equation, we see: \[ a + 2 = 3(a - 4) \]

None of the options are in exactly this form. However, we can match it with:

• \( a - 6 \):

The closest match is:

Answer: \( a + 2 = 3(a - 6 + 2) \)

This option can be simplified and checks out with the setup as it ultimately leads to the same relationship we derived.