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Finding the Third Proportional to 1,578 and 2,405

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Solution

The third proportional to 1,578 and 2,405 is: 3,665.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,578 : 2,405 = 2,405 : x
  2. Step 2: Convert to fraction form
    1,578/2,405 = 2,405/x
  3. Step 3: Cross multiply
    1,578x = 2,405 × 2,405
  4. Step 4: Simplify right side
    1,578x = 5,784,025
  5. Step 5: Solve for x
    x = 5,784,025/1,578
  6. Step 6: Final answer
    x = 3,665.42

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.