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Finding the Third Proportional to 298,596 and 463,014

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Solution

The third proportional to 298,596 and 463,014 is: 717,966.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    298,596 : 463,014 = 463,014 : x
  2. Step 2: Convert to fraction form
    298,596/463,014 = 463,014/x
  3. Step 3: Cross multiply
    298,596x = 463,014 × 463,014
  4. Step 4: Simplify right side
    298,596x = 214,381,964,196
  5. Step 5: Solve for x
    x = 214,381,964,196/298,596
  6. Step 6: Final answer
    x = 717,966.63

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.