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Finding the Third Proportional to 714 and 769.50

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Solution

The third proportional to 714 and 769.50 is: 829.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    714 : 769.50 = 769.50 : x
  2. Step 2: Convert to fraction form
    714/769.50 = 769.50/x
  3. Step 3: Cross multiply
    714x = 769.50 × 769.50
  4. Step 4: Simplify right side
    714x = 592,130.25
  5. Step 5: Solve for x
    x = 592,130.25/714
  6. Step 6: Final answer
    x = 829.31

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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.