A perfume manufacturer puts 16 fluid ounces in each bottle. How many gallons will fill 96 bottles?
The correct answer and explanation is:
First, let’s determine the total fluid ounces needed to fill 96 bottles, each containing 16 fluid ounces.
Total fluid ounces = Number of bottles × Fluid ounces per bottle
Total fluid ounces = 96 × 16
Total fluid ounces = 1536 fluid ounces
Next, convert fluid ounces to gallons. There are 128 fluid ounces in one gallon.
Gallons = Total fluid ounces ÷ Fluid ounces per gallon
Gallons = 1536 ÷ 128
Gallons = 12
Answer: 12 gallons are needed to fill 96 bottles.
Explanation:
To solve this problem, start by calculating the total amount of liquid required to fill all the bottles. Each bottle contains 16 fluid ounces, and there are 96 bottles. Multiplying these gives the total fluid ounces of perfume needed.
Next, to express this total volume in gallons, convert fluid ounces to gallons. The conversion factor is key: 1 gallon equals 128 fluid ounces. Dividing the total fluid ounces by 128 gives the equivalent volume in gallons.
This type of unit conversion is common in measurement problems involving liquids. It requires understanding the relationship between units and performing simple multiplication and division operations. Here, breaking down the problem into two steps—total volume calculation and unit conversion—helps ensure accuracy and clarity.
The process highlights the importance of knowing standard volume units and their equivalents, especially in contexts like manufacturing or packaging where precise quantities matter. By carefully converting units and multiplying correctly, the final answer accurately represents the total gallons of perfume required to fill all 96 bottles.