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Finding the Third Proportional to 782 and 1,035

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Solution

The third proportional to 782 and 1,035 is: 1,369.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 1,035 = 1,035 : x
  2. Step 2: Convert to fraction form
    782/1,035 = 1,035/x
  3. Step 3: Cross multiply
    782x = 1,035 × 1,035
  4. Step 4: Simplify right side
    782x = 1,071,225
  5. Step 5: Solve for x
    x = 1,071,225/782
  6. Step 6: Final answer
    x = 1,369.85

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.