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Finding the Third Proportional to 282,827 and 409,012

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Solution

The third proportional to 282,827 and 409,012 is: 591,495.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    282,827 : 409,012 = 409,012 : x
  2. Step 2: Convert to fraction form
    282,827/409,012 = 409,012/x
  3. Step 3: Cross multiply
    282,827x = 409,012 × 409,012
  4. Step 4: Simplify right side
    282,827x = 167,290,816,144
  5. Step 5: Solve for x
    x = 167,290,816,144/282,827
  6. Step 6: Final answer
    x = 591,495.21

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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.