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Finding the Third Proportional to 13,419 and 31,578

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Solution

The third proportional to 13,419 and 31,578 is: 74,310.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,419 : 31,578 = 31,578 : x
  2. Step 2: Convert to fraction form
    13,419/31,578 = 31,578/x
  3. Step 3: Cross multiply
    13,419x = 31,578 × 31,578
  4. Step 4: Simplify right side
    13,419x = 997,170,084
  5. Step 5: Solve for x
    x = 997,170,084/13,419
  6. Step 6: Final answer
    x = 74,310.31

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.