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Finding the Third Proportional to 32,098 and 77,324

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Solution

The third proportional to 32,098 and 77,324 is: 186,273.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,098 : 77,324 = 77,324 : x
  2. Step 2: Convert to fraction form
    32,098/77,324 = 77,324/x
  3. Step 3: Cross multiply
    32,098x = 77,324 × 77,324
  4. Step 4: Simplify right side
    32,098x = 5,979,000,976
  5. Step 5: Solve for x
    x = 5,979,000,976/32,098
  6. Step 6: Final answer
    x = 186,273.32

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.