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Finding the Third Proportional to 258 and 412

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Solution

The third proportional to 258 and 412 is: 657.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    258 : 412 = 412 : x
  2. Step 2: Convert to fraction form
    258/412 = 412/x
  3. Step 3: Cross multiply
    258x = 412 × 412
  4. Step 4: Simplify right side
    258x = 169,744
  5. Step 5: Solve for x
    x = 169,744/258
  6. Step 6: Final answer
    x = 657.92

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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.