Question

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?(

Answer 1

Let's define the ages of Andrea and Tony:

• 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 \( a + 2 \), 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:

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

This linear equation can be used to find Andrea’s and Tony’s current ages.

Answer 2

Answer Choices:

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 minus 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)

Answer 3

Let's analyze the problem step by step and match it with the provided choices.

1. Definitions:

   • Let \( a \) be Tony's current age.
   • Andrea's current age is \( a - 6 \).

2. Ages 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. Relationships:

   • In two years, Tony will be three times as old as Andrea: \[ a + 2 = 3(a - 4) \]

Now, let's compare this with the answer choices:

1. Choice 1: \( 3(a + 2) = a - 6 + 2 \)

   • This simplifies to \( 3(a + 2) = a - 4 \), which does not match our equation.

2. Choice 2: \( a + 2 = 3(a - 6 + 2) \)

   • This simplifies to \( a + 2 = 3(a - 4) \), which does match our derived equation.

3. Choice 3: \( a = 3(a + 2) \)

   • This does not match.

4. Choice 4: \( a + 2 = 3(a + 6 + 2) \)

   • This simplifies to \( a + 2 = 3(a + 8) \), which does not match.

From the analysis, the correct linear equation that can be used to find Andrea’s and Tony’s current ages is:

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