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Finding the Third Proportional to 97,658 and 209,140

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Solution

The third proportional to 97,658 and 209,140 is: 447,884.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,658 : 209,140 = 209,140 : x
  2. Step 2: Convert to fraction form
    97,658/209,140 = 209,140/x
  3. Step 3: Cross multiply
    97,658x = 209,140 × 209,140
  4. Step 4: Simplify right side
    97,658x = 43,739,539,600
  5. Step 5: Solve for x
    x = 43,739,539,600/97,658
  6. Step 6: Final answer
    x = 447,884.86

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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.