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Finding the Third Proportional to 414,693 and 659,403

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Solution

The third proportional to 414,693 and 659,403 is: 1,048,516.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,693 : 659,403 = 659,403 : x
  2. Step 2: Convert to fraction form
    414,693/659,403 = 659,403/x
  3. Step 3: Cross multiply
    414,693x = 659,403 × 659,403
  4. Step 4: Simplify right side
    414,693x = 434,812,316,409
  5. Step 5: Solve for x
    x = 434,812,316,409/414,693
  6. Step 6: Final answer
    x = 1,048,516.17

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.