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Finding the Third Proportional to 678 and 1,042

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Solution

The third proportional to 678 and 1,042 is: 1,601.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    678 : 1,042 = 1,042 : x
  2. Step 2: Convert to fraction form
    678/1,042 = 1,042/x
  3. Step 3: Cross multiply
    678x = 1,042 × 1,042
  4. Step 4: Simplify right side
    678x = 1,085,764
  5. Step 5: Solve for x
    x = 1,085,764/678
  6. Step 6: Final answer
    x = 1,601.42

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.