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Question

Difficulty: MediumDividing in a Ratio

A refueling truck contains 150150 gallons of aviation fuel. The fuel is distributed among three training aircraft in a ratio of 2:3:52:3:5. How many quarts of fuel does the second aircraft receive? (1 gallon=4 quarts1\text{ gallon} = 4\text{ quarts})

  1. A
    360
  2. B
    45
  3. 180Answer
  4. D
    300

Answer

180
The total number of ratio parts is 2+3+5=102 + 3 + 5 = 10. Dividing the total 150150 gallons by 1010 parts gives 1515 gallons per part. The second aircraft receives 33 parts, which is 3×15=453 \times 15 = 45 gallons. Converting to quarts, 45 gallons×4 quarts/gallon=180 quarts45 \text{ gallons} \times 4 \text{ quarts/gallon} = 180 \text{ quarts}.

Step-by-Step Solution

1
Calculate the total number of ratio parts.
2+3+5=102 + 3 + 5 = 10 parts
To find the value of a single part, we must divide the total amount by the sum of the ratio parts.
2
Determine the value of one part in gallons.
150÷10=15150 \div 10 = 15 gallons per part
This establishes the base unit for the ratio distribution.
3
Calculate the second aircraft's share in gallons.
3×15=453 \times 15 = 45 gallons
The second aircraft corresponds to the middle term in the 2:3:52:3:5 ratio, which is 33 parts.
4
Convert the share from gallons to quarts.
45×4=18045 \times 4 = 180 quarts
The question specifically asks for the final answer in quarts.

Key Concept

Dividing in a Ratio with Unit Conversions
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Topics

Dividing in a Ratio

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