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Finding the Third Proportional to 75,678 and 164,478

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Solution

The third proportional to 75,678 and 164,478 is: 357,475.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,678 : 164,478 = 164,478 : x
  2. Step 2: Convert to fraction form
    75,678/164,478 = 164,478/x
  3. Step 3: Cross multiply
    75,678x = 164,478 × 164,478
  4. Step 4: Simplify right side
    75,678x = 27,053,012,484
  5. Step 5: Solve for x
    x = 27,053,012,484/75,678
  6. Step 6: Final answer
    x = 357,475.26

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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.