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Finding the Third Proportional to 3,420 and 5,306

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Solution

The third proportional to 3,420 and 5,306 is: 8,232.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,420 : 5,306 = 5,306 : x
  2. Step 2: Convert to fraction form
    3,420/5,306 = 5,306/x
  3. Step 3: Cross multiply
    3,420x = 5,306 × 5,306
  4. Step 4: Simplify right side
    3,420x = 28,153,636
  5. Step 5: Solve for x
    x = 28,153,636/3,420
  6. Step 6: Final answer
    x = 8,232.06

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.