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Finding the Third Proportional to 589.50 and 649.13

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Solution

The third proportional to 589.50 and 649.13 is: 714.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    589.50 : 649.13 = 649.13 : x
  2. Step 2: Convert to fraction form
    589.50/649.13 = 649.13/x
  3. Step 3: Cross multiply
    589.50x = 649.13 × 649.13
  4. Step 4: Simplify right side
    589.50x = 421,363.27
  5. Step 5: Solve for x
    x = 421,363.27/589.50
  6. Step 6: Final answer
    x = 714.78

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.