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Finding the Third Proportional to 259 and 415.50

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Solution

The third proportional to 259 and 415.50 is: 666.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    259 : 415.50 = 415.50 : x
  2. Step 2: Convert to fraction form
    259/415.50 = 415.50/x
  3. Step 3: Cross multiply
    259x = 415.50 × 415.50
  4. Step 4: Simplify right side
    259x = 172,640.25
  5. Step 5: Solve for x
    x = 172,640.25/259
  6. Step 6: Final answer
    x = 666.56

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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.