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Finding the Third Proportional to 135,197 and 312,973

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Solution

The third proportional to 135,197 and 312,973 is: 724,513.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    135,197 : 312,973 = 312,973 : x
  2. Step 2: Convert to fraction form
    135,197/312,973 = 312,973/x
  3. Step 3: Cross multiply
    135,197x = 312,973 × 312,973
  4. Step 4: Simplify right side
    135,197x = 97,952,098,729
  5. Step 5: Solve for x
    x = 97,952,098,729/135,197
  6. Step 6: Final answer
    x = 724,513.85

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.