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Finding the Third Proportional to 5,702 and 8,506

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Solution

The third proportional to 5,702 and 8,506 is: 12,688.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,702 : 8,506 = 8,506 : x
  2. Step 2: Convert to fraction form
    5,702/8,506 = 8,506/x
  3. Step 3: Cross multiply
    5,702x = 8,506 × 8,506
  4. Step 4: Simplify right side
    5,702x = 72,352,036
  5. Step 5: Solve for x
    x = 72,352,036/5,702
  6. Step 6: Final answer
    x = 12,688.89

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.