Bradley owns b vedio game cartridges. IF Bradley's total is one - third the total owned by Andrew and four times the total owned by Charlie, how many video game catridges do the three of them own altogether, in terms of b?
(A) `(16)/(3)b`
(B) `(17)/(4)b`
(C) `(13)/(4)b`
(D) `(19)/(12)b`
(E) `(7)/(12)b`

Answer

To solve the problem step by step, we can follow this process:

### Step 1: Define the variables
Let:
- \( B \) = number of video game cartridges owned by Bradley.

### Step 2: Express Andrew's cartridges in terms of \( B \)
According to the problem, Bradley's total is one-third the total owned by Andrew. Therefore, we can express Andrew's cartridges as:
\[ \text{Andrew's cartridges} = 3B \]

### Step 3: Express Charlie's cartridges in terms of \( B \)
The problem also states that Bradley's total is four times the total owned by Charlie. Thus, we can express Charlie's cartridges as:
\[ \text{Charlie's cartridges} = \frac{1}{4}B \]

### Step 4: Calculate the total number of cartridges owned by all three
Now, we can find the total number of cartridges owned by Bradley, Andrew, and Charlie:
\[ \text{Total} = \text{Bradley's cartridges} + \text{Andrew's cartridges} + \text{Charlie's cartridges} \]
Substituting the values we have:
\[ \text{Total} = B + 3B + \frac{1}{4}B \]

### Step 5: Combine the terms
First, combine the terms \( B \) and \( 3B \):
\[ B + 3B = 4B \]
Now, add \( \frac{1}{4}B \) to \( 4B \):
\[ \text{Total} = 4B + \frac{1}{4}B \]

### Step 6: Find a common denominator
To add \( 4B \) and \( \frac{1}{4}B \), we need a common denominator. The common denominator is 4:
\[ 4B = \frac{16}{4}B \]
Now we can add:
\[ \text{Total} = \frac{16}{4}B + \frac{1}{4}B = \frac{17}{4}B \]

### Final Answer
Thus, the total number of video game cartridges owned by Bradley, Andrew, and Charlie is:
\[ \frac{17}{4}B \]

This matches with option (B).

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