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Finding the Third Proportional to 24,214 and 32,007

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Solution

The third proportional to 24,214 and 32,007 is: 42,308.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    24,214 : 32,007 = 32,007 : x
  2. Step 2: Convert to fraction form
    24,214/32,007 = 32,007/x
  3. Step 3: Cross multiply
    24,214x = 32,007 × 32,007
  4. Step 4: Simplify right side
    24,214x = 1,024,448,049
  5. Step 5: Solve for x
    x = 1,024,448,049/24,214
  6. Step 6: Final answer
    x = 42,308.09

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.