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Finding the Third Proportional to 51,142 and 77,505

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Solution

The third proportional to 51,142 and 77,505 is: 117,457.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,142 : 77,505 = 77,505 : x
  2. Step 2: Convert to fraction form
    51,142/77,505 = 77,505/x
  3. Step 3: Cross multiply
    51,142x = 77,505 × 77,505
  4. Step 4: Simplify right side
    51,142x = 6,007,025,025
  5. Step 5: Solve for x
    x = 6,007,025,025/51,142
  6. Step 6: Final answer
    x = 117,457.77

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.