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Finding the Third Proportional to 32,409 and 69,309

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Solution

The third proportional to 32,409 and 69,309 is: 148,222.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,409 : 69,309 = 69,309 : x
  2. Step 2: Convert to fraction form
    32,409/69,309 = 69,309/x
  3. Step 3: Cross multiply
    32,409x = 69,309 × 69,309
  4. Step 4: Simplify right side
    32,409x = 4,803,737,481
  5. Step 5: Solve for x
    x = 4,803,737,481/32,409
  6. Step 6: Final answer
    x = 148,222.33

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.