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Finding the Third Proportional to 57,414 and 83,854

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Solution

The third proportional to 57,414 and 83,854 is: 122,470.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    57,414 : 83,854 = 83,854 : x
  2. Step 2: Convert to fraction form
    57,414/83,854 = 83,854/x
  3. Step 3: Cross multiply
    57,414x = 83,854 × 83,854
  4. Step 4: Simplify right side
    57,414x = 7,031,493,316
  5. Step 5: Solve for x
    x = 7,031,493,316/57,414
  6. Step 6: Final answer
    x = 122,470.01

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.