To determine the rule for the number of people that can be transported by a certain number of ferries using the data provided, let’s analyze the number of ferries and their corresponding number of people transported:
- For 1 ferry: 7 people
- For 3 ferries: 19 people
- For 6 ferries: 37 people
- For 9 ferries: 55 people
- For 12 ferries: 73 people
Step 1: Identify the Pattern
The difference in people between each number of ferries helps us find the rule:
- From 1 to 3 ferries: \(19 - 7 = 12\)
- From 3 to 6 ferries: \(37 - 19 = 18\)
- From 6 to 9 ferries: \(55 - 37 = 18\)
- From 9 to 12 ferries: \(73 - 55 = 18\)
The first jump (from 1 to 3 ferries) is 12, and all subsequent jumps are consistent at 18.
It appears that each additional ferry after the first adds 18 people to the total. Thus, the pattern starts with 7 people for the first ferry, and the increments thereafter seem to be based on 18.
Step 2: Deriving the Rule
Starting at 7 people for the first ferry, the number of people can be expressed as: \[ \text{Number of people} = 7 + 18(n - 1) \] where \(n\) is the number of ferries.
This simplifies to: \[ \text{Number of people} = 18n - 11 \]
Step 3: Calculate for 15 Ferries
To check if 15 ferries can transport 93 people, substitute \(n = 15\) into the formula:
\[ \text{Number of people} = 18(15) - 11 = 270 - 11 = 259 \]
So, 15 ferries can transport 259 people.
Part B: Finding the Number of Ferries Needed to Transport 93 People
To find out how many ferries are needed to transport 93 people:
Using the equation derived earlier, we set: \[ 93 = 18n - 11 \]
Solving for \(n\): \[ 93 + 11 = 18n \] \[ 104 = 18n \] \[ n = \frac{104}{18} \approx 5.78 \]
Since the number of ferries must be a whole number, we round up to the nearest whole number, which is 6 ferries to transport at least 93 people.
Summary
Part A:
- The rule is: Add 18 people for each additional ferry, starting with 7 people for the first ferry.
- 15 ferries can transport 259 people.
Part B:
- The number of ferries needed to transport 93 people is approximately 6, meaning 6 ferries can transport 93 people.
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