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Finding the Third Proportional to 5,823 and 8,464

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Solution

The third proportional to 5,823 and 8,464 is: 12,302.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,823 : 8,464 = 8,464 : x
  2. Step 2: Convert to fraction form
    5,823/8,464 = 8,464/x
  3. Step 3: Cross multiply
    5,823x = 8,464 × 8,464
  4. Step 4: Simplify right side
    5,823x = 71,639,296
  5. Step 5: Solve for x
    x = 71,639,296/5,823
  6. Step 6: Final answer
    x = 12,302.82

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.