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Finding the Third Proportional to 20,534 and 31,420

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Solution

The third proportional to 20,534 and 31,420 is: 48,077.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,534 : 31,420 = 31,420 : x
  2. Step 2: Convert to fraction form
    20,534/31,420 = 31,420/x
  3. Step 3: Cross multiply
    20,534x = 31,420 × 31,420
  4. Step 4: Simplify right side
    20,534x = 987,216,400
  5. Step 5: Solve for x
    x = 987,216,400/20,534
  6. Step 6: Final answer
    x = 48,077.16

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.