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 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.