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Finding the Third Proportional to 821 and 1,410

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Solution

The third proportional to 821 and 1,410 is: 2,421.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    821 : 1,410 = 1,410 : x
  2. Step 2: Convert to fraction form
    821/1,410 = 1,410/x
  3. Step 3: Cross multiply
    821x = 1,410 × 1,410
  4. Step 4: Simplify right side
    821x = 1,988,100
  5. Step 5: Solve for x
    x = 1,988,100/821
  6. Step 6: Final answer
    x = 2,421.56

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Why These Related Problems?

These problems maintain the same ratio (1.72) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.