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Finding the Third Proportional to 32,076 and 47,970

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Solution

The third proportional to 32,076 and 47,970 is: 71,739.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,076 : 47,970 = 47,970 : x
  2. Step 2: Convert to fraction form
    32,076/47,970 = 47,970/x
  3. Step 3: Cross multiply
    32,076x = 47,970 × 47,970
  4. Step 4: Simplify right side
    32,076x = 2,301,120,900
  5. Step 5: Solve for x
    x = 2,301,120,900/32,076
  6. Step 6: Final answer
    x = 71,739.65

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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.