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Finding the Third Proportional to 5,972 and 13,946

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Solution

The third proportional to 5,972 and 13,946 is: 32,567.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,972 : 13,946 = 13,946 : x
  2. Step 2: Convert to fraction form
    5,972/13,946 = 13,946/x
  3. Step 3: Cross multiply
    5,972x = 13,946 × 13,946
  4. Step 4: Simplify right side
    5,972x = 194,490,916
  5. Step 5: Solve for x
    x = 194,490,916/5,972
  6. Step 6: Final answer
    x = 32,567.13

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.