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Finding the Third Proportional to 38,400 and 54,784

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Solution

The third proportional to 38,400 and 54,784 is: 78,158.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,400 : 54,784 = 54,784 : x
  2. Step 2: Convert to fraction form
    38,400/54,784 = 54,784/x
  3. Step 3: Cross multiply
    38,400x = 54,784 × 54,784
  4. Step 4: Simplify right side
    38,400x = 3,001,286,656
  5. Step 5: Solve for x
    x = 3,001,286,656/38,400
  6. Step 6: Final answer
    x = 78,158.51

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.