Sure, let's work through this problem step-by-step.
1. Understand the Problem:
We have a group of 3 people who want to buy a boat that costs [tex]$297. The goal is to determine how much each person should pay if they equally share the cost.
2. Identify the Type of Division Model:
There are three conceptual models of division:
- Repeated subtraction: This model involves repeatedly subtracting the divisor from the dividend until you reach zero. It’s often used when dealing with whole numbers and measuring how many times one number fits into another.
- Partition: This model involves dividing something into equal parts or groups. It’s often used when you need to split a total amount into equal shares.
- Missing factor: This model works on the principle that if \( a \times b = c \), then \( c \div a = b \). This is used when you need to find one of the factors given the product and the other factor.
3. Determine the Appropriate Model for the Problem:
Since the problem is about splitting the total cost ($[/tex]297) equally among the 3 people, we are partitioning the total amount into equal parts. Thus, the conceptual model that best fits this problem is the "partition" model.
4. Calculate Each Person's Share:
When you partition [tex]$297 into 3 equal parts, each person's share is calculated by dividing the total amount by the number of people:
\[
\text{Each person's share} = \frac{\text{Total cost}}{\text{Number of people}}
\]
Substituting the given values:
\[
\text{Each person's share} = \frac{297}{3} = 99
\]
5. Conclusion:
Therefore, when the $[/tex]297 cost of the boat is split equally among the 3 people, each person should pay [tex]$99. The problem corresponds to the "partition" model of division.
In summary, each person's share is $[/tex]99.0, and the conceptual model of division that best fits this problem is the "partition" model.
