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Finding the Third Proportional to 51,178 and 78,006

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Solution

The third proportional to 51,178 and 78,006 is: 118,897.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,178 : 78,006 = 78,006 : x
  2. Step 2: Convert to fraction form
    51,178/78,006 = 78,006/x
  3. Step 3: Cross multiply
    51,178x = 78,006 × 78,006
  4. Step 4: Simplify right side
    51,178x = 6,084,936,036
  5. Step 5: Solve for x
    x = 6,084,936,036/51,178
  6. Step 6: Final answer
    x = 118,897.50

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.