A Truck Holds At Most $20,000 \text{ Lb}$. There Are 18 Boxes On The Truck. Each Box Weighs $750 \text{ Lb}$. How Many Additional Boxes Can The Truck Hold? Graph The Solution And Show Your Work.

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Introduction

In this problem, we are given a truck with a weight limit of 20,000 lb20,000 \text{ lb}. The truck already has 18 boxes, each weighing 750 lb750 \text{ lb}. We need to find out how many additional boxes the truck can hold. To solve this problem, we will use basic algebra and graphing techniques.

Calculating the Total Weight of the Current Boxes

First, let's calculate the total weight of the current 18 boxes.

Total weight of current boxes=18×750 lb\text{Total weight of current boxes} = 18 \times 750 \text{ lb}

Total weight of current boxes=13,500 lb\text{Total weight of current boxes} = 13,500 \text{ lb}

Calculating the Remaining Weight Capacity of the Truck

Next, let's calculate the remaining weight capacity of the truck.

Remaining weight capacity=20,000 lb−13,500 lb\text{Remaining weight capacity} = 20,000 \text{ lb} - 13,500 \text{ lb}

Remaining weight capacity=6,500 lb\text{Remaining weight capacity} = 6,500 \text{ lb}

Calculating the Number of Additional Boxes the Truck Can Hold

Now, let's calculate the number of additional boxes the truck can hold.

Number of additional boxes=Remaining weight capacityWeight of each box\text{Number of additional boxes} = \frac{\text{Remaining weight capacity}}{\text{Weight of each box}}

Number of additional boxes=6,500 lb750 lb\text{Number of additional boxes} = \frac{6,500 \text{ lb}}{750 \text{ lb}}

Number of additional boxes=8.67\text{Number of additional boxes} = 8.67

Since we can't have a fraction of a box, we will round down to the nearest whole number.

Number of additional boxes=8\text{Number of additional boxes} = 8

Graphing the Solution

To visualize the solution, we can graph the weight capacity of the truck against the number of boxes.

Let's assume the weight capacity of the truck is represented by the function:

y=20,000−750xy = 20,000 - 750x

where xx is the number of boxes and yy is the weight capacity.

We can graph this function using a graphing tool or by plotting points.

Number of Boxes (xx) Weight Capacity (yy)
0 20,000
1 19,250
2 18,500
3 17,750
4 17,000
5 16,250
6 15,500
7 14,750
8 14,000
9 13,250
10 12,500
11 11,750
12 11,000
13 10,250
14 9,500
15 8,750
16 8,000
17 7,250
18 6,500

As we can see from the graph, the weight capacity of the truck decreases as the number of boxes increases. The truck can hold a maximum of 8 additional boxes before reaching its weight limit.

Conclusion

In this problem, we calculated the number of additional boxes a truck can hold given its weight limit and the weight of each box. We used basic algebra and graphing techniques to visualize the solution. The truck can hold a maximum of 8 additional boxes before reaching its weight limit.

References

Discussion

This problem is a classic example of a linear equation and graphing. The solution involves calculating the remaining weight capacity of the truck and dividing it by the weight of each box to find the number of additional boxes the truck can hold. The graph provides a visual representation of the solution and helps to illustrate the relationship between the number of boxes and the weight capacity of the truck.

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Introduction

In our previous article, we calculated the number of additional boxes a truck can hold given its weight limit and the weight of each box. We used basic algebra and graphing techniques to visualize the solution. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the weight limit of the truck?

A: The weight limit of the truck is 20,000 lb20,000 \text{ lb}.

Q: How many boxes are already on the truck?

A: There are 18 boxes already on the truck.

Q: What is the weight of each box?

A: Each box weighs 750 lb750 \text{ lb}.

Q: How many additional boxes can the truck hold?

A: The truck can hold a maximum of 8 additional boxes before reaching its weight limit.

Q: What is the remaining weight capacity of the truck?

A: The remaining weight capacity of the truck is 6,500 lb6,500 \text{ lb}.

Q: How do I calculate the number of additional boxes the truck can hold?

A: To calculate the number of additional boxes the truck can hold, you need to divide the remaining weight capacity by the weight of each box.

Q: What is the formula to calculate the number of additional boxes?

A: The formula to calculate the number of additional boxes is:

Number of additional boxes=Remaining weight capacityWeight of each box\text{Number of additional boxes} = \frac{\text{Remaining weight capacity}}{\text{Weight of each box}}

Q: Can I have a fraction of a box?

A: No, you can't have a fraction of a box. You need to round down to the nearest whole number.

Q: How do I graph the solution?

A: To graph the solution, you can use a graphing tool or plot points on a coordinate plane.

Q: What is the graph of the solution?

A: The graph of the solution is a linear equation that represents the weight capacity of the truck against the number of boxes.

Q: What is the equation of the graph?

A: The equation of the graph is:

y=20,000−750xy = 20,000 - 750x

where xx is the number of boxes and yy is the weight capacity.

Conclusion

In this article, we answered some frequently asked questions related to the problem of calculating the number of additional boxes a truck can hold given its weight limit and the weight of each box. We provided the weight limit of the truck, the number of boxes already on the truck, the weight of each box, and the remaining weight capacity of the truck. We also provided the formula to calculate the number of additional boxes and explained how to graph the solution.

References

Discussion

This article provides a comprehensive answer to some frequently asked questions related to the problem of calculating the number of additional boxes a truck can hold given its weight limit and the weight of each box. The article provides the weight limit of the truck, the number of boxes already on the truck, the weight of each box, and the remaining weight capacity of the truck. The article also provides the formula to calculate the number of additional boxes and explains how to graph the solution.

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