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Finding the Third Proportional to 120,770 and 177,462

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Solution

The third proportional to 120,770 and 177,462 is: 260,766.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,770 : 177,462 = 177,462 : x
  2. Step 2: Convert to fraction form
    120,770/177,462 = 177,462/x
  3. Step 3: Cross multiply
    120,770x = 177,462 × 177,462
  4. Step 4: Simplify right side
    120,770x = 31,492,761,444
  5. Step 5: Solve for x
    x = 31,492,761,444/120,770
  6. Step 6: Final answer
    x = 260,766.43

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.