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Finding the Third Proportional to 6,409 and 9,465

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Solution

The third proportional to 6,409 and 9,465 is: 13,978.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,409 : 9,465 = 9,465 : x
  2. Step 2: Convert to fraction form
    6,409/9,465 = 9,465/x
  3. Step 3: Cross multiply
    6,409x = 9,465 × 9,465
  4. Step 4: Simplify right side
    6,409x = 89,586,225
  5. Step 5: Solve for x
    x = 89,586,225/6,409
  6. Step 6: Final answer
    x = 13,978.19

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.