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Finding the Third Proportional to 407 and 840

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Solution

The third proportional to 407 and 840 is: 1,733.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    407 : 840 = 840 : x
  2. Step 2: Convert to fraction form
    407/840 = 840/x
  3. Step 3: Cross multiply
    407x = 840 × 840
  4. Step 4: Simplify right side
    407x = 705,600
  5. Step 5: Solve for x
    x = 705,600/407
  6. Step 6: Final answer
    x = 1,733.66

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.