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Finding the Third Proportional to 460 and 509

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Solution

The third proportional to 460 and 509 is: 563.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    460 : 509 = 509 : x
  2. Step 2: Convert to fraction form
    460/509 = 509/x
  3. Step 3: Cross multiply
    460x = 509 × 509
  4. Step 4: Simplify right side
    460x = 259,081
  5. Step 5: Solve for x
    x = 259,081/460
  6. Step 6: Final answer
    x = 563.22

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.