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Finding the Third Proportional to 7,830 and 17,408

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Solution

The third proportional to 7,830 and 17,408 is: 38,702.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 17,408 = 17,408 : x
  2. Step 2: Convert to fraction form
    7,830/17,408 = 17,408/x
  3. Step 3: Cross multiply
    7,830x = 17,408 × 17,408
  4. Step 4: Simplify right side
    7,830x = 303,038,464
  5. Step 5: Solve for x
    x = 303,038,464/7,830
  6. Step 6: Final answer
    x = 38,702.23

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.