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Finding the Third Proportional to 307,142 and 465,011

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Solution

The third proportional to 307,142 and 465,011 is: 704,023.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    307,142 : 465,011 = 465,011 : x
  2. Step 2: Convert to fraction form
    307,142/465,011 = 465,011/x
  3. Step 3: Cross multiply
    307,142x = 465,011 × 465,011
  4. Step 4: Simplify right side
    307,142x = 216,235,230,121
  5. Step 5: Solve for x
    x = 216,235,230,121/307,142
  6. Step 6: Final answer
    x = 704,023.64

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.