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Finding the Third Proportional to 278.25 and 409.31

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Solution

The third proportional to 278.25 and 409.31 is: 602.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    278.25 : 409.31 = 409.31 : x
  2. Step 2: Convert to fraction form
    278.25/409.31 = 409.31/x
  3. Step 3: Cross multiply
    278.25x = 409.31 × 409.31
  4. Step 4: Simplify right side
    278.25x = 167,536.72
  5. Step 5: Solve for x
    x = 167,536.72/278.25
  6. Step 6: Final answer
    x = 602.11

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.