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Finding the Third Proportional to 51,854 and 78,257

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Solution

The third proportional to 51,854 and 78,257 is: 118,103.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,854 : 78,257 = 78,257 : x
  2. Step 2: Convert to fraction form
    51,854/78,257 = 78,257/x
  3. Step 3: Cross multiply
    51,854x = 78,257 × 78,257
  4. Step 4: Simplify right side
    51,854x = 6,124,158,049
  5. Step 5: Solve for x
    x = 6,124,158,049/51,854
  6. Step 6: Final answer
    x = 118,103.87

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.