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Finding the Third Proportional to 83,670 and 117,031

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Solution

The third proportional to 83,670 and 117,031 is: 163,693.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,670 : 117,031 = 117,031 : x
  2. Step 2: Convert to fraction form
    83,670/117,031 = 117,031/x
  3. Step 3: Cross multiply
    83,670x = 117,031 × 117,031
  4. Step 4: Simplify right side
    83,670x = 13,696,254,961
  5. Step 5: Solve for x
    x = 13,696,254,961/83,670
  6. Step 6: Final answer
    x = 163,693.74

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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.