If 30 gallons of water weighs 249 pounds, what is the weight of 7 gallons of water in pounds?
The Correct Answer and Explanation is:
To determine the weight of 7 gallons of water based on the information provided, we can first calculate the weight of one gallon of water and then use that to find the weight of 7 gallons.
Step 1: Calculate the weight of one gallon of water
From the problem, we know that:
- 30 gallons of water weighs 249 pounds.
To find the weight of one gallon, we divide the total weight by the number of gallons:
[
\text{Weight of 1 gallon} = \frac{\text{Total weight}}{\text{Total gallons}} = \frac{249 \text{ pounds}}{30 \text{ gallons}} \approx 8.3 \text{ pounds per gallon}.
]
Step 2: Calculate the weight of 7 gallons of water
Now that we know the weight of one gallon, we can find the weight of 7 gallons by multiplying the weight of one gallon by 7:
[
\text{Weight of 7 gallons} = \text{Weight of 1 gallon} \times 7 = 8.3 \text{ pounds per gallon} \times 7 \text{ gallons} \approx 58.1 \text{ pounds}.
]
Conclusion
Therefore, the weight of 7 gallons of water is approximately 58.1 pounds.
Explanation of the Calculation Process
The calculation process involves understanding the relationship between volume (gallons) and weight (pounds) for water. Water has a relatively consistent density, which allows for straightforward conversions between volume and weight.
In this case, by starting with the total weight for a known volume (30 gallons), we established a unit rate (weight per gallon). This method is foundational in measurement conversions and is applicable to various substances where density is known.
Once we determined the weight of one gallon, we applied multiplication to find the weight of multiple gallons. This approach is efficient and practical in many real-world scenarios, including cooking, chemical mixing, and construction, where precise measurements are critical. Understanding how to break down the problem into manageable parts—first finding a unit rate and then scaling it—ensures accurate and effective calculations.