Question

The ages of four sisters are consecutive even integers. Two times the age of the youngest sister exceeds the oldest sister's age by 30 years. The equation 2x − (x + 6) = 30 models the age, x, of the youngest sister. What is the age of the oldest sister?
Responses

A 3030

B 3636

C 4242

D 4646

Answer 1

Let's analyze the equation you've provided:

The age of the youngest sister is represented as \( x \). Since the ages of the four sisters are consecutive even integers, the ages of the sisters can be expressed as:

- Youngest: \( x \)
- Second youngest: \( x + 2 \)
- Second oldest: \( x + 4 \)
- Oldest: \( x + 6 \)

According to the problem, two times the age of the youngest sister exceeds the oldest sister's age by 30 years. This is represented by the following equation:

\[
2x - (x + 6) = 30
\]

Now let's solve this equation for \( x \):

1. Distribute the terms in the equation:

\[
2x - x - 6 = 30
\]

2. Combine like terms:

\[
x - 6 = 30
\]

3. Add 6 to both sides:

\[
x = 36
\]

Now that we have determined the age of the youngest sister is \( 36 \), we can find the age of the oldest sister:

\[
\text{Oldest sister's age} = x + 6 = 36 + 6 = 42
\]

Thus, the age of the oldest sister is \( 42 \).

Looking at the responses you provided:

A: 30
B: 36
C: 42
D: 46

The correct answer is **C: 42**.