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Finding the Third Proportional to 469 and 821

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Solution

The third proportional to 469 and 821 is: 1,437.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    469 : 821 = 821 : x
  2. Step 2: Convert to fraction form
    469/821 = 821/x
  3. Step 3: Cross multiply
    469x = 821 × 821
  4. Step 4: Simplify right side
    469x = 674,041
  5. Step 5: Solve for x
    x = 674,041/469
  6. Step 6: Final answer
    x = 1,437.19

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Why These Related Problems?

These problems maintain the same ratio (1.75) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.