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Finding the Third Proportional to 406 and 1,078

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Solution

The third proportional to 406 and 1,078 is: 2,862.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    406 : 1,078 = 1,078 : x
  2. Step 2: Convert to fraction form
    406/1,078 = 1,078/x
  3. Step 3: Cross multiply
    406x = 1,078 × 1,078
  4. Step 4: Simplify right side
    406x = 1,162,084
  5. Step 5: Solve for x
    x = 1,162,084/406
  6. Step 6: Final answer
    x = 2,862.28

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Why These Related Problems?

These problems maintain the same ratio (2.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.