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Finding the Third Proportional to 97,786 and 146,896

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Solution

The third proportional to 97,786 and 146,896 is: 220,669.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,786 : 146,896 = 146,896 : x
  2. Step 2: Convert to fraction form
    97,786/146,896 = 146,896/x
  3. Step 3: Cross multiply
    97,786x = 146,896 × 146,896
  4. Step 4: Simplify right side
    97,786x = 21,578,434,816
  5. Step 5: Solve for x
    x = 21,578,434,816/97,786
  6. Step 6: Final answer
    x = 220,669.98

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.