Question

A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs \( x \) dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of \( x \)?

• A. \( \frac{x}{70} \)
• B. \( \frac{x}{35} \)
• C. \( \frac{3x}{70} \)
• D. \( \frac{3x}{10} \)
• E. \( \frac{3x}{7} \)

Hint:

To find the decrease in cost, calculate the difference in per person cost before and after the group size increases.

Answer 1

The Correct Option is B

Step 1: Initial cost per person for 7 fishermen.
The boat rental cost is \( x \) dollars for the day. With 7 fishermen, the cost per person is: \[ \text{Cost per person} = \frac{x}{7}. \] Step 2: Cost per person for 10 fishermen.
If 3 more fishermen join the group, there will be 10 fishermen in total. The new cost per person is: \[ \text{New cost per person} = \frac{x}{10}. \] Step 3: Calculate the difference in cost per person.
The difference in cost per person is: \[ \text{Difference} = \frac{x}{7} - \frac{x}{10}. \] To simplify the difference, find a common denominator: \[ \frac{x}{7} - \frac{x}{10} = \frac{10x}{70} - \frac{7x}{70} = \frac{3x}{70}. \] Step 4: Conclusion.
Thus, the rental cost per person decreases by \( \frac{3x}{70} \), and the correct answer is (B) \( \frac{x}{35} \).