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Finding the Third Proportional to 430,971 and 682,086

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Solution

The third proportional to 430,971 and 682,086 is: 1,079,518.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    430,971 : 682,086 = 682,086 : x
  2. Step 2: Convert to fraction form
    430,971/682,086 = 682,086/x
  3. Step 3: Cross multiply
    430,971x = 682,086 × 682,086
  4. Step 4: Simplify right side
    430,971x = 465,241,311,396
  5. Step 5: Solve for x
    x = 465,241,311,396/430,971
  6. Step 6: Final answer
    x = 1,079,518.83

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.