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Finding the Third Proportional to 27,309 and 31,820

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Solution

The third proportional to 27,309 and 31,820 is: 37,076.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,309 : 31,820 = 31,820 : x
  2. Step 2: Convert to fraction form
    27,309/31,820 = 31,820/x
  3. Step 3: Cross multiply
    27,309x = 31,820 × 31,820
  4. Step 4: Simplify right side
    27,309x = 1,012,512,400
  5. Step 5: Solve for x
    x = 1,012,512,400/27,309
  6. Step 6: Final answer
    x = 37,076.14

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.