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Finding the Third Proportional to 97,657 and 209,138

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Solution

The third proportional to 97,657 and 209,138 is: 447,880.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,657 : 209,138 = 209,138 : x
  2. Step 2: Convert to fraction form
    97,657/209,138 = 209,138/x
  3. Step 3: Cross multiply
    97,657x = 209,138 × 209,138
  4. Step 4: Simplify right side
    97,657x = 43,738,703,044
  5. Step 5: Solve for x
    x = 43,738,703,044/97,657
  6. Step 6: Final answer
    x = 447,880.88

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.