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Finding the Third Proportional to 14,024 and 32,770

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Solution

The third proportional to 14,024 and 32,770 is: 76,573.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,024 : 32,770 = 32,770 : x
  2. Step 2: Convert to fraction form
    14,024/32,770 = 32,770/x
  3. Step 3: Cross multiply
    14,024x = 32,770 × 32,770
  4. Step 4: Simplify right side
    14,024x = 1,073,872,900
  5. Step 5: Solve for x
    x = 1,073,872,900/14,024
  6. Step 6: Final answer
    x = 76,573.94

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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.