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Finding the Third Proportional to 51,205 and 77,523

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Solution

The third proportional to 51,205 and 77,523 is: 117,367.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,205 : 77,523 = 77,523 : x
  2. Step 2: Convert to fraction form
    51,205/77,523 = 77,523/x
  3. Step 3: Cross multiply
    51,205x = 77,523 × 77,523
  4. Step 4: Simplify right side
    51,205x = 6,009,815,529
  5. Step 5: Solve for x
    x = 6,009,815,529/51,205
  6. Step 6: Final answer
    x = 117,367.75

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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.