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Finding the Third Proportional to 259.69 and 411.09

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Solution

The third proportional to 259.69 and 411.09 is: 650.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    259.69 : 411.09 = 411.09 : x
  2. Step 2: Convert to fraction form
    259.69/411.09 = 411.09/x
  3. Step 3: Cross multiply
    259.69x = 411.09 × 411.09
  4. Step 4: Simplify right side
    259.69x = 168,998.07
  5. Step 5: Solve for x
    x = 168,998.07/259.69
  6. Step 6: Final answer
    x = 650.77

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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.