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Finding the Third Proportional to 782 and 1,840

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Solution

The third proportional to 782 and 1,840 is: 4,329.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 1,840 = 1,840 : x
  2. Step 2: Convert to fraction form
    782/1,840 = 1,840/x
  3. Step 3: Cross multiply
    782x = 1,840 × 1,840
  4. Step 4: Simplify right side
    782x = 3,385,600
  5. Step 5: Solve for x
    x = 3,385,600/782
  6. Step 6: Final answer
    x = 4,329.41

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.