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Finding the Third Proportional to 32,397 and 66,409

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Solution

The third proportional to 32,397 and 66,409 is: 136,128.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,397 : 66,409 = 66,409 : x
  2. Step 2: Convert to fraction form
    32,397/66,409 = 66,409/x
  3. Step 3: Cross multiply
    32,397x = 66,409 × 66,409
  4. Step 4: Simplify right side
    32,397x = 4,410,155,281
  5. Step 5: Solve for x
    x = 4,410,155,281/32,397
  6. Step 6: Final answer
    x = 136,128.51

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.