Linear Equations in Real-World Scenarios Quick Check

Question

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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

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

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

Answer 1

To solve this problem, let's first define the variables based on the given information:

• Let \( a \) be Tony's current age.
• Since Andrea is 6 years younger than Tony, her current age is \( a - 6 \).

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

Now let's match this with the options given:

1. \( a + 2 = 3(a - 6 + 2) \) simplifies to \( a + 2 = 3(a - 4) \). This is correct.
2. \( 3(a + 2) = a - 6 + 2 \) simplifies to \( 3(a + 2) = a - 4 \). This is incorrect.
3. \( a = 3(a + 2) \) is incorrect.
4. \( a + 2 = 3(a + 6 + 2) \) is incorrect.

The correct answer is: \( a + 2 = 3(a - 6 + 2) \)