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Finding the Third Proportional to 2,416 and 5,402

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Solution

The third proportional to 2,416 and 5,402 is: 12,078.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,416 : 5,402 = 5,402 : x
  2. Step 2: Convert to fraction form
    2,416/5,402 = 5,402/x
  3. Step 3: Cross multiply
    2,416x = 5,402 × 5,402
  4. Step 4: Simplify right side
    2,416x = 29,181,604
  5. Step 5: Solve for x
    x = 29,181,604/2,416
  6. Step 6: Final answer
    x = 12,078.48

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Why These Related Problems?

These problems maintain the same ratio (2.24) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.