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Finding the Third Proportional to 782 and 991.50

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Solution

The third proportional to 782 and 991.50 is: 1,257.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 991.50 = 991.50 : x
  2. Step 2: Convert to fraction form
    782/991.50 = 991.50/x
  3. Step 3: Cross multiply
    782x = 991.50 × 991.50
  4. Step 4: Simplify right side
    782x = 983,072.25
  5. Step 5: Solve for x
    x = 983,072.25/782
  6. Step 6: Final answer
    x = 1,257.13

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.