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Finding the Third Proportional to 97,306 and 209,162

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Solution

The third proportional to 97,306 and 209,162 is: 449,599.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,306 : 209,162 = 209,162 : x
  2. Step 2: Convert to fraction form
    97,306/209,162 = 209,162/x
  3. Step 3: Cross multiply
    97,306x = 209,162 × 209,162
  4. Step 4: Simplify right side
    97,306x = 43,748,742,244
  5. Step 5: Solve for x
    x = 43,748,742,244/97,306
  6. Step 6: Final answer
    x = 449,599.64

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.