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Finding the Third Proportional to 21,784 and 32,037

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Solution

The third proportional to 21,784 and 32,037 is: 47,115.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,784 : 32,037 = 32,037 : x
  2. Step 2: Convert to fraction form
    21,784/32,037 = 32,037/x
  3. Step 3: Cross multiply
    21,784x = 32,037 × 32,037
  4. Step 4: Simplify right side
    21,784x = 1,026,369,369
  5. Step 5: Solve for x
    x = 1,026,369,369/21,784
  6. Step 6: Final answer
    x = 47,115.74

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.