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Finding the Third Proportional to 417.84 and 649.59

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Solution

The third proportional to 417.84 and 649.59 is: 1,009.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    417.84 : 649.59 = 649.59 : x
  2. Step 2: Convert to fraction form
    417.84/649.59 = 649.59/x
  3. Step 3: Cross multiply
    417.84x = 649.59 × 649.59
  4. Step 4: Simplify right side
    417.84x = 421,972.04
  5. Step 5: Solve for x
    x = 421,972.04/417.84
  6. Step 6: Final answer
    x = 1,009.88

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.