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Finding the Third Proportional to 410,142 and 642,094

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Solution

The third proportional to 410,142 and 642,094 is: 1,005,224.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    410,142 : 642,094 = 642,094 : x
  2. Step 2: Convert to fraction form
    410,142/642,094 = 642,094/x
  3. Step 3: Cross multiply
    410,142x = 642,094 × 642,094
  4. Step 4: Simplify right side
    410,142x = 412,284,704,836
  5. Step 5: Solve for x
    x = 412,284,704,836/410,142
  6. Step 6: Final answer
    x = 1,005,224.30

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.