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Finding the Third Proportional to 398,046 and 596,823

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Solution

The third proportional to 398,046 and 596,823 is: 894,865.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    398,046 : 596,823 = 596,823 : x
  2. Step 2: Convert to fraction form
    398,046/596,823 = 596,823/x
  3. Step 3: Cross multiply
    398,046x = 596,823 × 596,823
  4. Step 4: Simplify right side
    398,046x = 356,197,693,329
  5. Step 5: Solve for x
    x = 356,197,693,329/398,046
  6. Step 6: Final answer
    x = 894,865.65

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.