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Finding the Third Proportional to 459 and 684.75

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Solution

The third proportional to 459 and 684.75 is: 1,021.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    459 : 684.75 = 684.75 : x
  2. Step 2: Convert to fraction form
    459/684.75 = 684.75/x
  3. Step 3: Cross multiply
    459x = 684.75 × 684.75
  4. Step 4: Simplify right side
    459x = 468,882.56
  5. Step 5: Solve for x
    x = 468,882.56/459
  6. Step 6: Final answer
    x = 1,021.53

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.