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Finding the Third Proportional to 75,742 and 164,022

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Solution

The third proportional to 75,742 and 164,022 is: 355,195.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,742 : 164,022 = 164,022 : x
  2. Step 2: Convert to fraction form
    75,742/164,022 = 164,022/x
  3. Step 3: Cross multiply
    75,742x = 164,022 × 164,022
  4. Step 4: Simplify right side
    75,742x = 26,903,216,484
  5. Step 5: Solve for x
    x = 26,903,216,484/75,742
  6. Step 6: Final answer
    x = 355,195.49

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.