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Finding the Third Proportional to 282,829 and 409,015

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Solution

The third proportional to 282,829 and 409,015 is: 591,499.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    282,829 : 409,015 = 409,015 : x
  2. Step 2: Convert to fraction form
    282,829/409,015 = 409,015/x
  3. Step 3: Cross multiply
    282,829x = 409,015 × 409,015
  4. Step 4: Simplify right side
    282,829x = 167,293,270,225
  5. Step 5: Solve for x
    x = 167,293,270,225/282,829
  6. Step 6: Final answer
    x = 591,499.71

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.