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Difficulty: MediumUS Customary Capacity and Volume

A public aquarium needs to treat a 120120-gallon quarantine tank with a specialized water conditioner. The treatment instructions require 33 fluid ounces of conditioner for every 44 gallons of water. The conditioner is sold only in 11-quart bottles. If the aquarium purchases the minimum number of full bottles required for the treatment, how many fluid ounces of conditioner will be left over after treating the tank?

  1. A
    0
  2. B
    2
  3. 6Answer
  4. D
    38

Answer

6
The correct answer is 66. First, calculate the total conditioner needed using the given proportion: (120 gallons÷4 gallons)×3 fluid ounces=90 fluid ounces(120 \text{ gallons} \div 4 \text{ gallons}) \times 3 \text{ fluid ounces} = 90 \text{ fluid ounces}. Next, convert the bottle capacity into fluid ounces so the units match: 1 quart=32 fluid ounces1 \text{ quart} = 32 \text{ fluid ounces}. To find the number of bottles required, divide the total needed by the bottle capacity: 90÷32=2.812590 \div 32 = 2.8125. Since the aquarium must purchase full bottles, they will need 33 bottles. The total volume of conditioner purchased is 3×32=963 \times 32 = 96 fluid ounces. Finally, subtract the needed amount from the purchased amount to find the leftover volume: 96−90=696 - 90 = 6 fluid ounces.

Step-by-Step Solution

1
Calculate the total fluid ounces of conditioner required for the tank.
9090 fluid ounces
The rate is 33 fluid ounces per 44 gallons. For a 120120-gallon tank, calculate (120÷4)×3=30×3=90(120 \div 4) \times 3 = 30 \times 3 = 90.
2
Convert the bottle size from quarts to fluid ounces.
3232 fluid ounces per bottle
Standard US Customary capacity conversions state that 11 quart is equal to 3232 fluid ounces.
3
Determine the minimum number of full bottles to purchase.
33 bottles
Divide the total needed by the bottle capacity: 90÷32=2.812590 \div 32 = 2.8125. Because they must buy full bottles, round up to the next whole number, which is 33.
4
Calculate the total fluid ounces purchased.
9696 fluid ounces
Multiply the number of bottles by the capacity per bottle: 3×32=963 \times 32 = 96.
5
Calculate the leftover volume of conditioner.
66 fluid ounces
Subtract the amount needed from the total amount purchased: 96−90=696 - 90 = 6.

Key Concept

Calculating liquid capacity required using proportional rates and converting standard US Customary units (quarts to fluid ounces) to determine purchasing requirements and remainders.
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Topics

US Customary Capacity and Volume

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