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Finding the Third Proportional to 654 and 1,412

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Solution

The third proportional to 654 and 1,412 is: 3,048.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    654 : 1,412 = 1,412 : x
  2. Step 2: Convert to fraction form
    654/1,412 = 1,412/x
  3. Step 3: Cross multiply
    654x = 1,412 × 1,412
  4. Step 4: Simplify right side
    654x = 1,993,744
  5. Step 5: Solve for x
    x = 1,993,744/654
  6. Step 6: Final answer
    x = 3,048.54

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.