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Finding the Third Proportional to 213,884 and 299,014

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Solution

The third proportional to 213,884 and 299,014 is: 418,027.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,884 : 299,014 = 299,014 : x
  2. Step 2: Convert to fraction form
    213,884/299,014 = 299,014/x
  3. Step 3: Cross multiply
    213,884x = 299,014 × 299,014
  4. Step 4: Simplify right side
    213,884x = 89,409,372,196
  5. Step 5: Solve for x
    x = 89,409,372,196/213,884
  6. Step 6: Final answer
    x = 418,027.40

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.