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Finding the Third Proportional to 259.14 and 415.05

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Solution

The third proportional to 259.14 and 415.05 is: 664.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    259.14 : 415.05 = 415.05 : x
  2. Step 2: Convert to fraction form
    259.14/415.05 = 415.05/x
  3. Step 3: Cross multiply
    259.14x = 415.05 × 415.05
  4. Step 4: Simplify right side
    259.14x = 172,263.10
  5. Step 5: Solve for x
    x = 172,263.10/259.14
  6. Step 6: Final answer
    x = 664.76

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.