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Finding the Third Proportional to 463,709 and 977,229

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Solution

The third proportional to 463,709 and 977,229 is: 2,059,430.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    463,709 : 977,229 = 977,229 : x
  2. Step 2: Convert to fraction form
    463,709/977,229 = 977,229/x
  3. Step 3: Cross multiply
    463,709x = 977,229 × 977,229
  4. Step 4: Simplify right side
    463,709x = 954,976,518,441
  5. Step 5: Solve for x
    x = 954,976,518,441/463,709
  6. Step 6: Final answer
    x = 2,059,430.63

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.