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Finding the Third Proportional to 37,471 and 78,407

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Solution

The third proportional to 37,471 and 78,407 is: 164,064.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,471 : 78,407 = 78,407 : x
  2. Step 2: Convert to fraction form
    37,471/78,407 = 78,407/x
  3. Step 3: Cross multiply
    37,471x = 78,407 × 78,407
  4. Step 4: Simplify right side
    37,471x = 6,147,657,649
  5. Step 5: Solve for x
    x = 6,147,657,649/37,471
  6. Step 6: Final answer
    x = 164,064.41

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.