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Finding the Third Proportional to 678 and 1,461

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Solution

The third proportional to 678 and 1,461 is: 3,148.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    678 : 1,461 = 1,461 : x
  2. Step 2: Convert to fraction form
    678/1,461 = 1,461/x
  3. Step 3: Cross multiply
    678x = 1,461 × 1,461
  4. Step 4: Simplify right side
    678x = 2,134,521
  5. Step 5: Solve for x
    x = 2,134,521/678
  6. Step 6: Final answer
    x = 3,148.26

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.