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Finding the Third Proportional to 4,102 and 7,412

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Solution

The third proportional to 4,102 and 7,412 is: 13,392.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,102 : 7,412 = 7,412 : x
  2. Step 2: Convert to fraction form
    4,102/7,412 = 7,412/x
  3. Step 3: Cross multiply
    4,102x = 7,412 × 7,412
  4. Step 4: Simplify right side
    4,102x = 54,937,744
  5. Step 5: Solve for x
    x = 54,937,744/4,102
  6. Step 6: Final answer
    x = 13,392.92

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Why These Related Problems?

These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.