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Finding the Third Proportional to 5,769 and 13,506

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Solution

The third proportional to 5,769 and 13,506 is: 31,619.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,769 : 13,506 = 13,506 : x
  2. Step 2: Convert to fraction form
    5,769/13,506 = 13,506/x
  3. Step 3: Cross multiply
    5,769x = 13,506 × 13,506
  4. Step 4: Simplify right side
    5,769x = 182,412,036
  5. Step 5: Solve for x
    x = 182,412,036/5,769
  6. Step 6: Final answer
    x = 31,619.35

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.