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Finding the Third Proportional to 12,324 and 17,414

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Solution

The third proportional to 12,324 and 17,414 is: 24,606.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,324 : 17,414 = 17,414 : x
  2. Step 2: Convert to fraction form
    12,324/17,414 = 17,414/x
  3. Step 3: Cross multiply
    12,324x = 17,414 × 17,414
  4. Step 4: Simplify right side
    12,324x = 303,247,396
  5. Step 5: Solve for x
    x = 303,247,396/12,324
  6. Step 6: Final answer
    x = 24,606.25

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.