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Finding the Third Proportional to 14,564 and 23,097

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Solution

The third proportional to 14,564 and 23,097 is: 36,629.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,564 : 23,097 = 23,097 : x
  2. Step 2: Convert to fraction form
    14,564/23,097 = 23,097/x
  3. Step 3: Cross multiply
    14,564x = 23,097 × 23,097
  4. Step 4: Simplify right side
    14,564x = 533,471,409
  5. Step 5: Solve for x
    x = 533,471,409/14,564
  6. Step 6: Final answer
    x = 36,629.46

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.