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Finding the Third Proportional to 31,534 and 66,911

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Solution

The third proportional to 31,534 and 66,911 is: 141,976.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,534 : 66,911 = 66,911 : x
  2. Step 2: Convert to fraction form
    31,534/66,911 = 66,911/x
  3. Step 3: Cross multiply
    31,534x = 66,911 × 66,911
  4. Step 4: Simplify right side
    31,534x = 4,477,081,921
  5. Step 5: Solve for x
    x = 4,477,081,921/31,534
  6. Step 6: Final answer
    x = 141,976.34

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.