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Finding the Third Proportional to 209,000 and 313,013

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Solution

The third proportional to 209,000 and 313,013 is: 468,790.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,000 : 313,013 = 313,013 : x
  2. Step 2: Convert to fraction form
    209,000/313,013 = 313,013/x
  3. Step 3: Cross multiply
    209,000x = 313,013 × 313,013
  4. Step 4: Simplify right side
    209,000x = 97,977,138,169
  5. Step 5: Solve for x
    x = 97,977,138,169/209,000
  6. Step 6: Final answer
    x = 468,790.13

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.