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)**