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Finding the Third Proportional to 194,096 and 411,521

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Solution

The third proportional to 194,096 and 411,521 is: 872,503.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    194,096 : 411,521 = 411,521 : x
  2. Step 2: Convert to fraction form
    194,096/411,521 = 411,521/x
  3. Step 3: Cross multiply
    194,096x = 411,521 × 411,521
  4. Step 4: Simplify right side
    194,096x = 169,349,533,441
  5. Step 5: Solve for x
    x = 169,349,533,441/194,096
  6. Step 6: Final answer
    x = 872,503.98

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.