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Finding the Third Proportional to 213,796 and 461,824

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Solution

The third proportional to 213,796 and 461,824 is: 997,593.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,796 : 461,824 = 461,824 : x
  2. Step 2: Convert to fraction form
    213,796/461,824 = 461,824/x
  3. Step 3: Cross multiply
    213,796x = 461,824 × 461,824
  4. Step 4: Simplify right side
    213,796x = 213,281,406,976
  5. Step 5: Solve for x
    x = 213,281,406,976/213,796
  6. Step 6: Final answer
    x = 997,593.07

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.