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Finding the Third Proportional to 12,024 and 14,076

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Solution

The third proportional to 12,024 and 14,076 is: 16,478.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,024 : 14,076 = 14,076 : x
  2. Step 2: Convert to fraction form
    12,024/14,076 = 14,076/x
  3. Step 3: Cross multiply
    12,024x = 14,076 × 14,076
  4. Step 4: Simplify right side
    12,024x = 198,133,776
  5. Step 5: Solve for x
    x = 198,133,776/12,024
  6. Step 6: Final answer
    x = 16,478.19

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.