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Finding the Third Proportional to 864 and 1,407

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Solution

The third proportional to 864 and 1,407 is: 2,291.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    864 : 1,407 = 1,407 : x
  2. Step 2: Convert to fraction form
    864/1,407 = 1,407/x
  3. Step 3: Cross multiply
    864x = 1,407 × 1,407
  4. Step 4: Simplify right side
    864x = 1,979,649
  5. Step 5: Solve for x
    x = 1,979,649/864
  6. Step 6: Final answer
    x = 2,291.26

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.