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Finding the Third Proportional to 840 and 1,657

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Solution

The third proportional to 840 and 1,657 is: 3,268.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    840 : 1,657 = 1,657 : x
  2. Step 2: Convert to fraction form
    840/1,657 = 1,657/x
  3. Step 3: Cross multiply
    840x = 1,657 × 1,657
  4. Step 4: Simplify right side
    840x = 2,745,649
  5. Step 5: Solve for x
    x = 2,745,649/840
  6. Step 6: Final answer
    x = 3,268.63

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.