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Finding the Third Proportional to 21,421 and 32,013

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Solution

The third proportional to 21,421 and 32,013 is: 47,842.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,421 : 32,013 = 32,013 : x
  2. Step 2: Convert to fraction form
    21,421/32,013 = 32,013/x
  3. Step 3: Cross multiply
    21,421x = 32,013 × 32,013
  4. Step 4: Simplify right side
    21,421x = 1,024,832,169
  5. Step 5: Solve for x
    x = 1,024,832,169/21,421
  6. Step 6: Final answer
    x = 47,842.41

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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.