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Finding the Third Proportional to 657.75 and 709.50

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Solution

The third proportional to 657.75 and 709.50 is: 765.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    657.75 : 709.50 = 709.50 : x
  2. Step 2: Convert to fraction form
    657.75/709.50 = 709.50/x
  3. Step 3: Cross multiply
    657.75x = 709.50 × 709.50
  4. Step 4: Simplify right side
    657.75x = 503,390.25
  5. Step 5: Solve for x
    x = 503,390.25/657.75
  6. Step 6: Final answer
    x = 765.32

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.