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Finding the Third Proportional to 864 and 2,074

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Solution

The third proportional to 864 and 2,074 is: 4,978.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    864 : 2,074 = 2,074 : x
  2. Step 2: Convert to fraction form
    864/2,074 = 2,074/x
  3. Step 3: Cross multiply
    864x = 2,074 × 2,074
  4. Step 4: Simplify right side
    864x = 4,301,476
  5. Step 5: Solve for x
    x = 4,301,476/864
  6. Step 6: Final answer
    x = 4,978.56

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.