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Finding the Third Proportional to 75,724 and 106,184

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Solution

The third proportional to 75,724 and 106,184 is: 148,896.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,724 : 106,184 = 106,184 : x
  2. Step 2: Convert to fraction form
    75,724/106,184 = 106,184/x
  3. Step 3: Cross multiply
    75,724x = 106,184 × 106,184
  4. Step 4: Simplify right side
    75,724x = 11,275,041,856
  5. Step 5: Solve for x
    x = 11,275,041,856/75,724
  6. Step 6: Final answer
    x = 148,896.54

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.