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Finding the Third Proportional to 409.70 and 649.07

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Solution

The third proportional to 409.70 and 649.07 is: 1,028.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.70 : 649.07 = 649.07 : x
  2. Step 2: Convert to fraction form
    409.70/649.07 = 649.07/x
  3. Step 3: Cross multiply
    409.70x = 649.07 × 649.07
  4. Step 4: Simplify right side
    409.70x = 421,289.10
  5. Step 5: Solve for x
    x = 421,289.10/409.70
  6. Step 6: Final answer
    x = 1,028.28

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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.