On average, seawater contains approximately 1.2 ounces of salt per liter. How many gallons of seawater, to the nearest tenth of a gallon, would contain 2.5 pounds of salt?
The Correct Answer and Explanation is:
First, begin by organizing the given information and setting up unit conversions to solve the problem:
- Seawater contains approximately 1.2 ounces of salt per liter.
- The target is 2.5 pounds of salt.
- The task is to find out how many gallons of seawater contain this amount of salt.
Step 1: Convert pounds to ounces
Since 1 pound equals 16 ounces:2.5 pounds×16 ounces/pound=40 ounces2.5 \, \text{pounds} \times 16 \, \text{ounces/pound} = 40 \, \text{ounces}2.5pounds×16ounces/pound=40ounces
Thus, 2.5 pounds equals 40 ounces of salt.
Step 2: Determine how many liters of seawater are needed
Given that each liter contains 1.2 ounces of salt:Liters=40 ounces1.2 ounces/liter=33.3‾ liters\text{Liters} = \frac{40 \, \text{ounces}}{1.2 \, \text{ounces/liter}} = 33.\overline{3} \, \text{liters}Liters=1.2ounces/liter40ounces=33.3liters
So, approximately 33.33 liters of seawater are required.
Step 3: Convert liters to gallons
Using the conversion factor where 1 gallon equals 3.78541 liters:Gallons=33.33 liters3.78541 liters/gallon≈8.8 gallons\text{Gallons} = \frac{33.33 \, \text{liters}}{3.78541 \, \text{liters/gallon}} \approx 8.8 \, \text{gallons}Gallons=3.78541liters/gallon33.33liters≈8.8gallons
Final Answer:
Approximately 8.8 gallons of seawater would contain 2.5 pounds of salt.
Explanation:
The problem involves converting between units of mass and volume. The amount of salt is first standardized into ounces to match the concentration given in ounces per liter. After determining the total number of liters necessary to contain the desired salt mass, a final conversion to gallons provides the required volume in familiar units. Precision during conversion ensures the accuracy of the final result, which is rounded to the nearest tenth of a gallon as requested.
