Problem 311 - Elementary Algebra

Question

In the following exercises, solve. A water taxi has a maximum load of 1,800 pounds. If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi?

Step-by-Step Solution

Answer

12 people can safely ride in the water taxi.

Step 1: Identify the maximum load

The water taxi has a maximum load capacity of 1,800 pounds.

Step 2: Identify the average weight per person

The average weight of one person is given as 150 pounds.

Step 3: Set up the equation

To find out how many people can safely ride in the water taxi, set up the equation as follows: \text{Maximum load} = \text{Number of people} \times \text{Average weight per person}Let the number of people be represented by the variable \( n \). The equation will be:1800 = 150n

Step 4: Solve for the number of people

Isolate the variable \( n \) by dividing both sides of the equation by 150:\[ n = \frac{1800}{150} \] Calculate the division:\[ n = 12 \]

Step 5: Interpret the result

The calculation shows that 12 people can safely ride in the water taxi without exceeding the maximum load of 1,800 pounds.

Key Concepts

Algebraic Equations

In this exercise, we use an algebraic equation. An algebraic equation helps us understand relationships between different quantities by using letters (or variables) to represent numbers. Here, we want to find out how many people can safely ride in the water taxi. We know the total weight allowed and the weight per person. We represent the number of people with the variable \( n \). By setting up the equation \( 1800 = 150n \), we can solve for \( n \), which tells us the number of people. This process of translating a word problem into a mathematical equation is crucial to solving many real-world problems.

Weight Distribution

Weight distribution refers to how weight is spread across different people or objects. In this problem, we distribute the total allowed weight of the water taxi among the people riding it. Each person adds their weight to the total. If the average weight is 150 pounds, we need to see how many such 150-pound units (people) can fit into the total allowed weight of 1,800 pounds. Proper weight distribution ensures that the load is manageable and the limits are not exceeded. This understanding helps us avoid overloading, which can lead to safety issues.

Safe Load Calculation

Safe load calculation is about determining the maximum amount of weight that can be carried without risking safety. In the problem, the water taxi can carry up to 1,800 pounds safely. By knowing that each person weighs approximately 150 pounds, we calculate the maximum number of people by dividing the total load capacity by the weight per person. Using the equation, we find out:

• Maximum load = 1,800 pounds
• Weight per person = 150 pounds

This calculation ensures that the number of people (12) will not exceed the safe load, keeping everyone safe.

Problem-Solving Steps

Problem-solving involves breaking down the main problem into smaller, manageable steps. For this exercise, the steps are:

• Identify the total weight capacity.
• Know the average weight per person.
• Set up an algebraic equation to represent the problem.
• Solve the equation for the variable representing the number of people.
• Interpret the result to ensure it makes sense practically.

Following these steps helps us solve problems methodically. By isolating each part of the problem and solving it step-by-step, we ensure accuracy and clarity in our solution.