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Finding the Third Proportional to 51,684 and 81,974

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Solution

The third proportional to 51,684 and 81,974 is: 130,015.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,684 : 81,974 = 81,974 : x
  2. Step 2: Convert to fraction form
    51,684/81,974 = 81,974/x
  3. Step 3: Cross multiply
    51,684x = 81,974 × 81,974
  4. Step 4: Simplify right side
    51,684x = 6,719,736,676
  5. Step 5: Solve for x
    x = 6,719,736,676/51,684
  6. Step 6: Final answer
    x = 130,015.80

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.