To solve the problem systematically, we will follow these steps:
Step 1: Understand the Problem
- The original roller coaster can hold 30 passengers, with an average weight of 160 pounds per passenger.
- New safety standards have lowered the maximum number of passengers by 5.
- We need to find out how much a full load of passengers would weigh under the new limit, while keeping the average weight per passenger the same.
Step 2: Identify Variables and Create an Expression
Let:
- \( P \) = number of passengers (after the safety standard change)
- \( W \) = average weight of each passenger
Given:
- Original number of passengers = 30
- Average weight = 160 pounds
- New maximum number of passengers = 30 - 5 = 25
Thus, we can write the expression for the total weight under the new limit as: \[ \text{Total Weight} = P \times W \]
Step 3: Substitute the Known Values
We know at the new limit:
- \( P = 25 \)
- \( W = 160 \)
Now we substitute these values into the expression: \[ \text{Total Weight} = 25 \times 160 \]
Step 4: Evaluate the Expression
Now we will calculate the total weight: \[ \text{Total Weight} = 25 \times 160 \] Doing the multiplication: \[ 25 \times 160 = 4000 \]
Conclusion
The total weight of a full load of passengers under the new limit is 4000 pounds.
So, the complete evaluation shows that the expression accurately represents the weight of the passengers under the new safety standards.
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