Select The Correct Answer From Each Drop-down Menu.Jordan Is Tracking A Recent Online Purchase. The Shipping Costs State That The Item Will Be Shipped In A 24-inch Long Box With A Volume Of 2,880 Cubic Inches. The Width Of The Box Is Seven Inches Less
Jordan's Online Purchase: A Math Problem
Jordan is tracking a recent online purchase, and the shipping costs state that the item will be shipped in a 24-inch long box with a volume of 2,880 cubic inches. The width of the box is seven inches less than the length, and the height is unknown. To determine the correct dimensions of the box, we need to use the formula for the volume of a rectangular prism, which is given by:
Volume = Length × Width × Height
Step 1: Understand the Given Information
- The length of the box is 24 inches.
- The volume of the box is 2,880 cubic inches.
- The width of the box is seven inches less than the length.
Step 2: Express the Width in Terms of the Length
Since the width is seven inches less than the length, we can express the width as:
Width = Length - 7
Step 3: Substitute the Width Expression into the Volume Formula
Substituting the width expression into the volume formula, we get:
2,880 = 24 × (Length - 7) × Height
Step 4: Simplify the Equation
Simplifying the equation, we get:
2,880 = 24 × Length × Height - 168 × Height
Step 5: Rearrange the Equation
Rearranging the equation to isolate the term involving the height, we get:
24 × Length × Height - 2,880 = -168 × Height
Step 6: Factor Out the Height
Factoring out the height, we get:
Height (24 × Length - 168) = 2,880
Step 7: Solve for the Height
Solving for the height, we get:
Height = 2,880 / (24 × Length - 168)
Step 8: Substitute the Length Value
Substituting the length value of 24 inches into the height equation, we get:
Height = 2,880 / (24 × 24 - 168)
Step 9: Simplify the Equation
Simplifying the equation, we get:
Height = 2,880 / (576 - 168)
Step 10: Calculate the Height
Calculating the height, we get:
Height = 2,880 / 408
Height = 7.059
Step 11: Round the Height Value
Rounding the height value to the nearest whole number, we get:
Height = 7 inches
Step 12: Calculate the Width
Now that we have the height value, we can calculate the width using the expression:
Width = Length - 7
Substituting the length value of 24 inches into the width expression, we get:
Width = 24 - 7
Width = 17 inches
Step 13: Verify the Volume
To verify the volume, we can multiply the length, width, and height values:
Volume = Length × Width × Height
Substituting the length, width, and height values, we get:
Volume = 24 × 17 × 7
Volume = 2,884
The calculated volume is very close to the given volume of 2,880 cubic inches.
Conclusion
In conclusion, the dimensions of the box are:
- Length: 24 inches
- Width: 17 inches
- Height: 7 inches
Frequently Asked Questions
Q: What is the problem about?
A: The problem is about calculating the dimensions of a box based on its volume and length. The box has a volume of 2,880 cubic inches and a length of 24 inches.
Q: What is the relationship between the width and length of the box?
A: The width of the box is seven inches less than the length.
Q: How can we calculate the height of the box?
A: We can use the formula for the volume of a rectangular prism, which is given by:
Volume = Length × Width × Height
We can rearrange this formula to solve for the height:
Height = Volume / (Length × Width)
Q: How can we calculate the width of the box?
A: We can use the expression:
Width = Length - 7
Q: What is the height of the box?
A: The height of the box is approximately 7 inches.
Q: What is the width of the box?
A: The width of the box is 17 inches.
Q: How can we verify the volume of the box?
A: We can multiply the length, width, and height values to calculate the volume:
Volume = Length × Width × Height
Q: What is the volume of the box?
A: The volume of the box is approximately 2,884 cubic inches.
Q: Is the calculated volume close to the given volume?
A: Yes, the calculated volume is very close to the given volume of 2,880 cubic inches.
Q: What are the dimensions of the box?
A: The dimensions of the box are:
- Length: 24 inches
- Width: 17 inches
- Height: 7 inches
Q: How can we use this problem to practice our math skills?
A: We can use this problem to practice our skills in:
- Understanding the formula for the volume of a rectangular prism
- Rearranging equations to solve for unknown variables
- Calculating dimensions based on given information
- Verifying calculations using different methods
Q: What are some real-world applications of this problem?
A: This problem has real-world applications in:
- Shipping and logistics: Calculating the dimensions of packages to ensure they fit in shipping containers
- Architecture: Designing buildings and structures with specific dimensions and volumes
- Engineering: Calculating the dimensions of machines and equipment to ensure they fit in designated spaces
Q: How can we extend this problem to make it more challenging?
A: We can extend this problem by:
- Adding more variables to the equation
- Changing the shape of the box (e.g., from a rectangular prism to a cylinder)
- Introducing constraints on the dimensions (e.g., the length must be at least 20 inches)
By extending this problem, we can make it more challenging and interesting, while still practicing our math skills.