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Finding the Third Proportional to 697.50 and 758.25

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Solution

The third proportional to 697.50 and 758.25 is: 824.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    697.50 : 758.25 = 758.25 : x
  2. Step 2: Convert to fraction form
    697.50/758.25 = 758.25/x
  3. Step 3: Cross multiply
    697.50x = 758.25 × 758.25
  4. Step 4: Simplify right side
    697.50x = 574,943.06
  5. Step 5: Solve for x
    x = 574,943.06/697.50
  6. Step 6: Final answer
    x = 824.29

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.