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Finding the Third Proportional to 5,827 and 9,023

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Solution

The third proportional to 5,827 and 9,023 is: 13,971.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,827 : 9,023 = 9,023 : x
  2. Step 2: Convert to fraction form
    5,827/9,023 = 9,023/x
  3. Step 3: Cross multiply
    5,827x = 9,023 × 9,023
  4. Step 4: Simplify right side
    5,827x = 81,414,529
  5. Step 5: Solve for x
    x = 81,414,529/5,827
  6. Step 6: Final answer
    x = 13,971.95

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.