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Finding the Third Proportional to 21,413 and 32,011

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Solution

The third proportional to 21,413 and 32,011 is: 47,854.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,413 : 32,011 = 32,011 : x
  2. Step 2: Convert to fraction form
    21,413/32,011 = 32,011/x
  3. Step 3: Cross multiply
    21,413x = 32,011 × 32,011
  4. Step 4: Simplify right side
    21,413x = 1,024,704,121
  5. Step 5: Solve for x
    x = 1,024,704,121/21,413
  6. Step 6: Final answer
    x = 47,854.30

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.