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Finding the Third Proportional to 138,024 and 209,106

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Solution

The third proportional to 138,024 and 209,106 is: 316,795.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    138,024 : 209,106 = 209,106 : x
  2. Step 2: Convert to fraction form
    138,024/209,106 = 209,106/x
  3. Step 3: Cross multiply
    138,024x = 209,106 × 209,106
  4. Step 4: Simplify right side
    138,024x = 43,725,319,236
  5. Step 5: Solve for x
    x = 43,725,319,236/138,024
  6. Step 6: Final answer
    x = 316,795.04

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.