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Question

Difficulty: MediumUS Customary Capacity and Volume

An auto detailing shop keeps different formulations of car wash soap in various containers. To properly inventory their stock, the manager asks a technician to arrange 44 containers based on their capacity.

Arrange the following containers in order from the smallest volume to the largest volume.

  1. 155 quarts
  2. 21111 pints
  3. 31.51.5 gallons
  4. 4200200 fluid ounces

Answer

The correct sequence from smallest to largest is: 55 quarts, 1111 pints, 1.51.5 gallons, and 200200 fluid ounces.
By converting every measurement to fluid ounces, we find the exact comparative sizes: 55 quarts equals 160160 fluid ounces, 1111 pints equals 176176 fluid ounces, 1.51.5 gallons equals 192192 fluid ounces, and the final container is exactly 200200 fluid ounces. Arranging these calculated amounts from smallest to largest gives the correct sequence.

Step-by-Step Solution

1
Identify the conversion factors needed to change all units to the smallest unit given, which is fluid ounces.
1 gallon=128 fluid ounces1 \text{ gallon} = 128 \text{ fluid ounces}, 1 quart=32 fluid ounces1 \text{ quart} = 32 \text{ fluid ounces}, and 1 pint=16 fluid ounces1 \text{ pint} = 16 \text{ fluid ounces}.
To accurately compare different volumes, they must all be converted to a single common unit.
2
Convert the volume of the quarts container into fluid ounces.
5 quarts×32 fluid ounces/quart=160 fluid ounces5 \text{ quarts} \times 32 \text{ fluid ounces/quart} = 160 \text{ fluid ounces}.
Standardizing the unit for accurate comparison.
3
Convert the volume of the pints container into fluid ounces.
11 pints×16 fluid ounces/pint=176 fluid ounces11 \text{ pints} \times 16 \text{ fluid ounces/pint} = 176 \text{ fluid ounces}.
Standardizing the unit for accurate comparison.
4
Convert the volume of the gallons container into fluid ounces.
1.5 gallons×128 fluid ounces/gallon=192 fluid ounces1.5 \text{ gallons} \times 128 \text{ fluid ounces/gallon} = 192 \text{ fluid ounces}.
Standardizing the unit for accurate comparison.
5
Compare all four quantities in fluid ounces and order them from smallest to largest.
160 fl oz<176 fl oz<192 fl oz<200 fl oz160 \text{ fl oz} < 176 \text{ fl oz} < 192 \text{ fl oz} < 200 \text{ fl oz}.
Sorting the standard numerical values provides the final, correct arrangement.

Key Concept

Converting various US customary volume measurements into a common unit to compare and order capacities.
Estimated Time:1m 30s
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Topics

US Customary Capacity and Volume

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