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

Answer 1

To solve the problem, we can first define the ages in terms of Tony's current age \( a \):

- Tony's current age: \( a \)
- Andrea's current age: \( a - 6 \) (since Andrea is 6 years younger than Tony)

In two years, their ages will be:
- Tony's age in two years: \( a + 2 \)
- Andrea's age in two years: \( (a - 6) + 2 = a - 4 \)

According to the problem, in two years, Tony will be three times as old as Andrea. This can be expressed as:

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

Now, let's simplify this equation:

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

2. Rearranging the equation gives:
\[ a + 2 - 3a + 12 = 0 \]
\[ -2a + 14 = 0 \]
\[ 2a = 14 \]
\[ a = 7 \]

This indicates Tony's current age is \( 7 \) years. Andrea's current age then is:
\[ 7 - 6 = 1 \]

Now, let's find the equation among the given options that matches our derived equation:

The original equation can be expressed as:
\[ a + 2 = 3(a - 4) \]
But, we also notice that:
\[ a + 2 = 3(a - 6 + 2) \]
is the same as substituting \( (a - 6 + 2) = (a - 4) \).

Hence, the correct equation that can be used to find Andrea's and Tony's current ages from the provided options is:

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

So the answer is:
**a + 2 = 3(a - 6 + 2)**