`{:("Column A" , "Park, Jack, and Galvin distributed","ColumnB"),(, "prize money of 120 dollars among",),(, "themselves. Park received 3/10 of",),(,"what Jack and Galvin together",),(,"received. Jack received 3/11 of",),(,"what park and Galvin together received",),("The amount received by Park", ,"The amount received by Jack"):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem of how Park, Jack, and Galvin distributed the prize money of $120, we will set up equations based on the information given in the question.

### Step 1: Define Variables
Let:
- \( X \) = Amount received by Park
- \( Y \) = Amount received by Jack
- \( Z \) = Amount received by Galvin

### Step 2: Set Up the First Equation
According to the problem, Park received \( \frac{3}{10} \) of what Jack and Galvin together received. This can be expressed as:
\[ X = \frac{3}{10}(Y + Z) \]
Multiplying both sides by 10 to eliminate the fraction gives:
\[ 10X = 3(Y + Z) \]
This simplifies to:
\[ 10X = 3Y + 3Z \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
Next, it is stated that Jack received \( \frac{3}{11} \) of what Park and Galvin together received. This can be expressed as:
\[ Y = \frac{3}{11}(X + Z) \]
Multiplying both sides by 11 gives:
\[ 11Y = 3(X + Z) \]
This simplifies to:
\[ 11Y = 3X + 3Z \quad \text{(Equation 2)} \]

### Step 4: Add the Two Equations
Now we will add Equation 1 and Equation 2:
\[ 10X - 3Y - 3Z + 3X - 11Y + 3Z = 0 \]
This simplifies to:
\[ 13X - 14Y = 0 \]
Rearranging gives:
\[ 13X = 14Y \]
Thus, we can express \( X \) in terms of \( Y \):
\[ X = \frac{14}{13}Y \]

### Step 5: Compare \( X \) and \( Y \)
Now we need to compare \( X \) and \( Y \):
Since \( \frac{14}{13} > 1 \), it follows that:
\[ X > Y \]
This indicates that the amount received by Park is greater than the amount received by Jack.

### Step 6: Conclusion
Since \( X \) (the amount received by Park) is greater than \( Y \) (the amount received by Jack), we conclude that:
- The amount received by Park (Column A) is larger than the amount received by Jack (Column B).

Thus, the correct option is:
**Option 1: Column A is larger.**