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Finding the Third Proportional to 83,454 and 128,097

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Solution

The third proportional to 83,454 and 128,097 is: 196,621.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,454 : 128,097 = 128,097 : x
  2. Step 2: Convert to fraction form
    83,454/128,097 = 128,097/x
  3. Step 3: Cross multiply
    83,454x = 128,097 × 128,097
  4. Step 4: Simplify right side
    83,454x = 16,408,841,409
  5. Step 5: Solve for x
    x = 16,408,841,409/83,454
  6. Step 6: Final answer
    x = 196,621.39

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.