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Finding the Third Proportional to 209,569 and 314,367

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Solution

The third proportional to 209,569 and 314,367 is: 471,570.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,569 : 314,367 = 314,367 : x
  2. Step 2: Convert to fraction form
    209,569/314,367 = 314,367/x
  3. Step 3: Cross multiply
    209,569x = 314,367 × 314,367
  4. Step 4: Simplify right side
    209,569x = 98,826,610,689
  5. Step 5: Solve for x
    x = 98,826,610,689/209,569
  6. Step 6: Final answer
    x = 471,570.75

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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.