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Finding the Third Proportional to 523 and 787

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Solution

The third proportional to 523 and 787 is: 1,184.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 787 = 787 : x
  2. Step 2: Convert to fraction form
    523/787 = 787/x
  3. Step 3: Cross multiply
    523x = 787 × 787
  4. Step 4: Simplify right side
    523x = 619,369
  5. Step 5: Solve for x
    x = 619,369/523
  6. Step 6: Final answer
    x = 1,184.26

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.