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Finding the Third Proportional to 78,006 and 117,561

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Solution

The third proportional to 78,006 and 117,561 is: 177,173.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    78,006 : 117,561 = 117,561 : x
  2. Step 2: Convert to fraction form
    78,006/117,561 = 117,561/x
  3. Step 3: Cross multiply
    78,006x = 117,561 × 117,561
  4. Step 4: Simplify right side
    78,006x = 13,820,588,721
  5. Step 5: Solve for x
    x = 13,820,588,721/78,006
  6. Step 6: Final answer
    x = 177,173.41

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.