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Question

Difficulty: MediumBasic Ratios

A medical logistics unit prepares field trauma kits. The weight ratio of bandages to antiseptic solution in each bulk shipment is strictly maintained at 3:43:4. If a particular shipment contains 1212 pounds of bandages, what is the required weight of the antiseptic solution in ounces?

  1. A
    16
  2. 256Answer
  3. C
    64
  4. D
    144

Answer

The correct weight of the antiseptic solution is 256 ounces.
The ratio of bandages to antiseptic is 3:43:4. Since 1212 pounds of bandages represents 33 parts of the ratio, each part is equal to 44 pounds (12÷3=412 \div 3 = 4). The antiseptic represents 44 parts, so its weight is 4×4=164 \times 4 = 16 pounds. Finally, to find the weight in ounces, multiply by 1616 (since there are 1616 ounces in a standard pound), yielding 16×16=25616 \times 16 = 256 ounces.

Step-by-Step Solution

1
Set up a proportion using the given ratio of bandages to antiseptic (3:43:4).
34=12x\frac{3}{4} = \frac{12}{x}
The weight of the items must maintain the specific part-to-part ratio given in the problem.
2
Solve for xx to find the weight of the antiseptic in pounds.
3x=48⇒x=163x = 48 \Rightarrow x = 16 pounds
Cross-multiplying and dividing isolates the unknown quantity of antiseptic.
3
Convert the weight of the antiseptic from pounds to ounces.
16 pounds×16 ounces/pound=256 ounces16 \text{ pounds} \times 16 \text{ ounces/pound} = 256 \text{ ounces}
The question explicitly requests the final answer in ounces.

Key Concept

Solving basic ratios and applying unit conversions.
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Topics

Basic Ratios

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