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Finding the Third Proportional to 32,072 and 47,964

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Solution

The third proportional to 32,072 and 47,964 is: 71,730.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,072 : 47,964 = 47,964 : x
  2. Step 2: Convert to fraction form
    32,072/47,964 = 47,964/x
  3. Step 3: Cross multiply
    32,072x = 47,964 × 47,964
  4. Step 4: Simplify right side
    32,072x = 2,300,545,296
  5. Step 5: Solve for x
    x = 2,300,545,296/32,072
  6. Step 6: Final answer
    x = 71,730.65

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.