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Finding the Third Proportional to 209,998 and 460,823

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Solution

The third proportional to 209,998 and 460,823 is: 1,011,237.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,998 : 460,823 = 460,823 : x
  2. Step 2: Convert to fraction form
    209,998/460,823 = 460,823/x
  3. Step 3: Cross multiply
    209,998x = 460,823 × 460,823
  4. Step 4: Simplify right side
    209,998x = 212,357,837,329
  5. Step 5: Solve for x
    x = 212,357,837,329/209,998
  6. Step 6: Final answer
    x = 1,011,237.43

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.