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Finding the Third Proportional to 821 and 1,313

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Solution

The third proportional to 821 and 1,313 is: 2,099.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    821 : 1,313 = 1,313 : x
  2. Step 2: Convert to fraction form
    821/1,313 = 1,313/x
  3. Step 3: Cross multiply
    821x = 1,313 × 1,313
  4. Step 4: Simplify right side
    821x = 1,723,969
  5. Step 5: Solve for x
    x = 1,723,969/821
  6. Step 6: Final answer
    x = 2,099.84

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.