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Finding the Third Proportional to 75,830 and 165,106

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Solution

The third proportional to 75,830 and 165,106 is: 359,488.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,830 : 165,106 = 165,106 : x
  2. Step 2: Convert to fraction form
    75,830/165,106 = 165,106/x
  3. Step 3: Cross multiply
    75,830x = 165,106 × 165,106
  4. Step 4: Simplify right side
    75,830x = 27,259,991,236
  5. Step 5: Solve for x
    x = 27,259,991,236/75,830
  6. Step 6: Final answer
    x = 359,488.21

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.