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Finding the Third Proportional to 102,769 and 153,733

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Solution

The third proportional to 102,769 and 153,733 is: 229,970.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,769 : 153,733 = 153,733 : x
  2. Step 2: Convert to fraction form
    102,769/153,733 = 153,733/x
  3. Step 3: Cross multiply
    102,769x = 153,733 × 153,733
  4. Step 4: Simplify right side
    102,769x = 23,633,835,289
  5. Step 5: Solve for x
    x = 23,633,835,289/102,769
  6. Step 6: Final answer
    x = 229,970.47

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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.