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Finding the Third Proportional to 213,097 and 323,533

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Solution

The third proportional to 213,097 and 323,533 is: 491,201.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,097 : 323,533 = 323,533 : x
  2. Step 2: Convert to fraction form
    213,097/323,533 = 323,533/x
  3. Step 3: Cross multiply
    213,097x = 323,533 × 323,533
  4. Step 4: Simplify right side
    213,097x = 104,673,602,089
  5. Step 5: Solve for x
    x = 104,673,602,089/213,097
  6. Step 6: Final answer
    x = 491,201.67

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.