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Finding the Third Proportional to 9,509 and 14,264

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Solution

The third proportional to 9,509 and 14,264 is: 21,396.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,509 : 14,264 = 14,264 : x
  2. Step 2: Convert to fraction form
    9,509/14,264 = 14,264/x
  3. Step 3: Cross multiply
    9,509x = 14,264 × 14,264
  4. Step 4: Simplify right side
    9,509x = 203,461,696
  5. Step 5: Solve for x
    x = 203,461,696/9,509
  6. Step 6: Final answer
    x = 21,396.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.