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Finding the Third Proportional to 509 and 585

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Solution

The third proportional to 509 and 585 is: 672.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 585 = 585 : x
  2. Step 2: Convert to fraction form
    509/585 = 585/x
  3. Step 3: Cross multiply
    509x = 585 × 585
  4. Step 4: Simplify right side
    509x = 342,225
  5. Step 5: Solve for x
    x = 342,225/509
  6. Step 6: Final answer
    x = 672.35

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.