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Finding the Third Proportional to 506 and 659

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Solution

The third proportional to 506 and 659 is: 858.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    506 : 659 = 659 : x
  2. Step 2: Convert to fraction form
    506/659 = 659/x
  3. Step 3: Cross multiply
    506x = 659 × 659
  4. Step 4: Simplify right side
    506x = 434,281
  5. Step 5: Solve for x
    x = 434,281/506
  6. Step 6: Final answer
    x = 858.26

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.