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Finding the Third Proportional to 83,013 and 128,409

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Solution

The third proportional to 83,013 and 128,409 is: 198,629.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,013 : 128,409 = 128,409 : x
  2. Step 2: Convert to fraction form
    83,013/128,409 = 128,409/x
  3. Step 3: Cross multiply
    83,013x = 128,409 × 128,409
  4. Step 4: Simplify right side
    83,013x = 16,488,871,281
  5. Step 5: Solve for x
    x = 16,488,871,281/83,013
  6. Step 6: Final answer
    x = 198,629.99

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.