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Finding the Third Proportional to 51,407 and 76,684

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Solution

The third proportional to 51,407 and 76,684 is: 114,389.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,407 : 76,684 = 76,684 : x
  2. Step 2: Convert to fraction form
    51,407/76,684 = 76,684/x
  3. Step 3: Cross multiply
    51,407x = 76,684 × 76,684
  4. Step 4: Simplify right side
    51,407x = 5,880,435,856
  5. Step 5: Solve for x
    x = 5,880,435,856/51,407
  6. Step 6: Final answer
    x = 114,389.79

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.