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Finding the Third Proportional to 821 and 1,597

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Solution

The third proportional to 821 and 1,597 is: 3,106.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    821 : 1,597 = 1,597 : x
  2. Step 2: Convert to fraction form
    821/1,597 = 1,597/x
  3. Step 3: Cross multiply
    821x = 1,597 × 1,597
  4. Step 4: Simplify right side
    821x = 2,550,409
  5. Step 5: Solve for x
    x = 2,550,409/821
  6. Step 6: Final answer
    x = 3,106.47

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.