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Finding the Third Proportional to 5,802 and 13,533

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Solution

The third proportional to 5,802 and 13,533 is: 31,565.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,802 : 13,533 = 13,533 : x
  2. Step 2: Convert to fraction form
    5,802/13,533 = 13,533/x
  3. Step 3: Cross multiply
    5,802x = 13,533 × 13,533
  4. Step 4: Simplify right side
    5,802x = 183,142,089
  5. Step 5: Solve for x
    x = 183,142,089/5,802
  6. Step 6: Final answer
    x = 31,565.34

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.