Questions: 52. Vanessa read some books over the holidays. Eve read three times as many books as Vanessa. Altogether they read 24 books. How many more books did Eve read than Vanessa? A) 6 B) 12 C) 24 D) 30

52. Vanessa read some books over the holidays. Eve read three times as many books as Vanessa. Altogether they read 24 books. How many more books did Eve read than Vanessa? A) 6 B) 12 C) 24 D) 30
Transcript text: 52. Vanessa read some books over the holidays. Eve read three times as many books as Vanessa. Altogether they read 24 books. How many more books did Eve read than Vanessa? A) 6 B) 12 C) 24 D) 30
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Solution

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Solution Steps

Step 1: Define Variables

Let \( V \) represent the number of books Vanessa read.
Let \( E \) represent the number of books Eve read.

Step 2: Set Up Equations

From the problem:

  1. Eve read three times as many books as Vanessa:
    \( E = 3V \).
  2. Together, they read 24 books:
    \( V + E = 24 \).
Step 3: Substitute and Solve

Substitute \( E = 3V \) into the second equation:
\( V + 3V = 24 \).
Simplify:
\( 4V = 24 \).
Divide both sides by 4:
\( V = 6 \).

Now, substitute \( V = 6 \) into \( E = 3V \):
\( E = 3(6) = 18 \).

Step 4: Find the Difference

Calculate how many more books Eve read than Vanessa:
\( E - V = 18 - 6 = 12 \).

Final Answer

\(\boxed{12}\)

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