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Finding the Third Proportional to 3,416 and 5,409

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Solution

The third proportional to 3,416 and 5,409 is: 8,564.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,416 : 5,409 = 5,409 : x
  2. Step 2: Convert to fraction form
    3,416/5,409 = 5,409/x
  3. Step 3: Cross multiply
    3,416x = 5,409 × 5,409
  4. Step 4: Simplify right side
    3,416x = 29,257,281
  5. Step 5: Solve for x
    x = 29,257,281/3,416
  6. Step 6: Final answer
    x = 8,564.78

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.