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Finding the Third Proportional to 8,216 and 19,784

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Solution

The third proportional to 8,216 and 19,784 is: 47,639.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,216 : 19,784 = 19,784 : x
  2. Step 2: Convert to fraction form
    8,216/19,784 = 19,784/x
  3. Step 3: Cross multiply
    8,216x = 19,784 × 19,784
  4. Step 4: Simplify right side
    8,216x = 391,406,656
  5. Step 5: Solve for x
    x = 391,406,656/8,216
  6. Step 6: Final answer
    x = 47,639.56

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.