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Finding the Third Proportional to 211,998 and 463,842

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Solution

The third proportional to 211,998 and 463,842 is: 1,014,865.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    211,998 : 463,842 = 463,842 : x
  2. Step 2: Convert to fraction form
    211,998/463,842 = 463,842/x
  3. Step 3: Cross multiply
    211,998x = 463,842 × 463,842
  4. Step 4: Simplify right side
    211,998x = 215,149,400,964
  5. Step 5: Solve for x
    x = 215,149,400,964/211,998
  6. Step 6: Final answer
    x = 1,014,865.24

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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.