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

Question

A a+2=3(a-6+2)
B a+2=3(a+6+2)
C a=3(a+2)
D 3(a+2)=a-6+2

Answer 1

Let's denote Andrea's current age as \( a - 6 \), since she is 6 years younger than Tony, who is \( a \) years old.

In two years, Tony's age will be \( a + 2 \) and Andrea's age will be \( (a - 6) + 2 = a - 4 \).

According to the problem, in two years, Tony's age will be three times Andrea's age:

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

Now, let's look at the options provided:

A. \( a + 2 = 3(a - 6 + 2) \)
B. \( a + 2 = 3(a + 6 + 2) \)
C. \( a = 3(a + 2) \)
D. \( 3(a + 2) = a - 6 + 2 \)

Let's simplify option A to see if it matches with our derived equation: \[ 3(a - 6 + 2) = 3(a - 4) \quad \text{(which matches our derived equation)} \] So, option A is actually valid.

Now let's analyze the others:

• Option B is incorrect because it does not correctly represent Andrea's age.
• Option C is incorrect because it doesn’t reflect the relationship described in the problem.
• Option D is incorrect because it rearranges the terms inaccurately regarding ages.

The correct answer is:

A. \( a + 2 = 3(a - 6 + 2) \)