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Finding the Third Proportional to 5,970 and 14,142

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Solution

The third proportional to 5,970 and 14,142 is: 33,500.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,970 : 14,142 = 14,142 : x
  2. Step 2: Convert to fraction form
    5,970/14,142 = 14,142/x
  3. Step 3: Cross multiply
    5,970x = 14,142 × 14,142
  4. Step 4: Simplify right side
    5,970x = 199,996,164
  5. Step 5: Solve for x
    x = 199,996,164/5,970
  6. Step 6: Final answer
    x = 33,500.19

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.