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Finding the Third Proportional to 5,840 and 13,770

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Solution

The third proportional to 5,840 and 13,770 is: 32,467.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,840 : 13,770 = 13,770 : x
  2. Step 2: Convert to fraction form
    5,840/13,770 = 13,770/x
  3. Step 3: Cross multiply
    5,840x = 13,770 × 13,770
  4. Step 4: Simplify right side
    5,840x = 189,612,900
  5. Step 5: Solve for x
    x = 189,612,900/5,840
  6. Step 6: Final answer
    x = 32,467.96

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.