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Finding the Third Proportional to 382,849 and 563,216

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Solution

The third proportional to 382,849 and 563,216 is: 828,557.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    382,849 : 563,216 = 563,216 : x
  2. Step 2: Convert to fraction form
    382,849/563,216 = 563,216/x
  3. Step 3: Cross multiply
    382,849x = 563,216 × 563,216
  4. Step 4: Simplify right side
    382,849x = 317,212,262,656
  5. Step 5: Solve for x
    x = 317,212,262,656/382,849
  6. Step 6: Final answer
    x = 828,557.11

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.