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Finding the Third Proportional to 197,784 and 314,462

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Solution

The third proportional to 197,784 and 314,462 is: 499,971.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,784 : 314,462 = 314,462 : x
  2. Step 2: Convert to fraction form
    197,784/314,462 = 314,462/x
  3. Step 3: Cross multiply
    197,784x = 314,462 × 314,462
  4. Step 4: Simplify right side
    197,784x = 98,886,349,444
  5. Step 5: Solve for x
    x = 98,886,349,444/197,784
  6. Step 6: Final answer
    x = 499,971.43

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.