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Finding the Third Proportional to 97,840 and 209,504

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Solution

The third proportional to 97,840 and 209,504 is: 448,609.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,840 : 209,504 = 209,504 : x
  2. Step 2: Convert to fraction form
    97,840/209,504 = 209,504/x
  3. Step 3: Cross multiply
    97,840x = 209,504 × 209,504
  4. Step 4: Simplify right side
    97,840x = 43,891,926,016
  5. Step 5: Solve for x
    x = 43,891,926,016/97,840
  6. Step 6: Final answer
    x = 448,609.22

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.