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Finding the Third Proportional to 13,142 and 19,657

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Solution

The third proportional to 13,142 and 19,657 is: 29,401.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,142 : 19,657 = 19,657 : x
  2. Step 2: Convert to fraction form
    13,142/19,657 = 19,657/x
  3. Step 3: Cross multiply
    13,142x = 19,657 × 19,657
  4. Step 4: Simplify right side
    13,142x = 386,397,649
  5. Step 5: Solve for x
    x = 386,397,649/13,142
  6. Step 6: Final answer
    x = 29,401.74

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.