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Finding the Third Proportional to 5,314 and 8,539

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Solution

The third proportional to 5,314 and 8,539 is: 13,721.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,314 : 8,539 = 8,539 : x
  2. Step 2: Convert to fraction form
    5,314/8,539 = 8,539/x
  3. Step 3: Cross multiply
    5,314x = 8,539 × 8,539
  4. Step 4: Simplify right side
    5,314x = 72,914,521
  5. Step 5: Solve for x
    x = 72,914,521/5,314
  6. Step 6: Final answer
    x = 13,721.21

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.