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Finding the Third Proportional to 261.38 and 412.31

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Solution

The third proportional to 261.38 and 412.31 is: 650.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    261.38 : 412.31 = 412.31 : x
  2. Step 2: Convert to fraction form
    261.38/412.31 = 412.31/x
  3. Step 3: Cross multiply
    261.38x = 412.31 × 412.31
  4. Step 4: Simplify right side
    261.38x = 170,001.60
  5. Step 5: Solve for x
    x = 170,001.60/261.38
  6. Step 6: Final answer
    x = 650.41

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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.