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Finding the Third Proportional to 51,780 and 78,075

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Solution

The third proportional to 51,780 and 78,075 is: 117,723.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,780 : 78,075 = 78,075 : x
  2. Step 2: Convert to fraction form
    51,780/78,075 = 78,075/x
  3. Step 3: Cross multiply
    51,780x = 78,075 × 78,075
  4. Step 4: Simplify right side
    51,780x = 6,095,705,625
  5. Step 5: Solve for x
    x = 6,095,705,625/51,780
  6. Step 6: Final answer
    x = 117,723.17

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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.