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Finding the Third Proportional to 782 and 906

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Solution

The third proportional to 782 and 906 is: 1,049.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 906 = 906 : x
  2. Step 2: Convert to fraction form
    782/906 = 906/x
  3. Step 3: Cross multiply
    782x = 906 × 906
  4. Step 4: Simplify right side
    782x = 820,836
  5. Step 5: Solve for x
    x = 820,836/782
  6. Step 6: Final answer
    x = 1,049.66

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.