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Finding the Third Proportional to 11,600 and 12,784

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Solution

The third proportional to 11,600 and 12,784 is: 14,088.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    11,600 : 12,784 = 12,784 : x
  2. Step 2: Convert to fraction form
    11,600/12,784 = 12,784/x
  3. Step 3: Cross multiply
    11,600x = 12,784 × 12,784
  4. Step 4: Simplify right side
    11,600x = 163,430,656
  5. Step 5: Solve for x
    x = 163,430,656/11,600
  6. Step 6: Final answer
    x = 14,088.85

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.