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Finding the Third Proportional to 83,154 and 128,011

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Solution

The third proportional to 83,154 and 128,011 is: 197,065.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,154 : 128,011 = 128,011 : x
  2. Step 2: Convert to fraction form
    83,154/128,011 = 128,011/x
  3. Step 3: Cross multiply
    83,154x = 128,011 × 128,011
  4. Step 4: Simplify right side
    83,154x = 16,386,816,121
  5. Step 5: Solve for x
    x = 16,386,816,121/83,154
  6. Step 6: Final answer
    x = 197,065.88

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.