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Finding the Third Proportional to 10,830 and 11,784

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Solution

The third proportional to 10,830 and 11,784 is: 12,822.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,830 : 11,784 = 11,784 : x
  2. Step 2: Convert to fraction form
    10,830/11,784 = 11,784/x
  3. Step 3: Cross multiply
    10,830x = 11,784 × 11,784
  4. Step 4: Simplify right side
    10,830x = 138,862,656
  5. Step 5: Solve for x
    x = 138,862,656/10,830
  6. Step 6: Final answer
    x = 12,822.04

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.