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Finding the Third Proportional to 83,677 and 117,307

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Solution

The third proportional to 83,677 and 117,307 is: 164,452.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,677 : 117,307 = 117,307 : x
  2. Step 2: Convert to fraction form
    83,677/117,307 = 117,307/x
  3. Step 3: Cross multiply
    83,677x = 117,307 × 117,307
  4. Step 4: Simplify right side
    83,677x = 13,760,932,249
  5. Step 5: Solve for x
    x = 13,760,932,249/83,677
  6. Step 6: Final answer
    x = 164,452.98

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.