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Finding the Third Proportional to 97,749 and 214,209

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Solution

The third proportional to 97,749 and 214,209 is: 469,421.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,749 : 214,209 = 214,209 : x
  2. Step 2: Convert to fraction form
    97,749/214,209 = 214,209/x
  3. Step 3: Cross multiply
    97,749x = 214,209 × 214,209
  4. Step 4: Simplify right side
    97,749x = 45,885,495,681
  5. Step 5: Solve for x
    x = 45,885,495,681/97,749
  6. Step 6: Final answer
    x = 469,421.64

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.