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Finding the Third Proportional to 289,423 and 412,852

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Solution

The third proportional to 289,423 and 412,852 is: 588,919.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    289,423 : 412,852 = 412,852 : x
  2. Step 2: Convert to fraction form
    289,423/412,852 = 412,852/x
  3. Step 3: Cross multiply
    289,423x = 412,852 × 412,852
  4. Step 4: Simplify right side
    289,423x = 170,446,773,904
  5. Step 5: Solve for x
    x = 170,446,773,904/289,423
  6. Step 6: Final answer
    x = 588,919.24

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.