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Finding the Third Proportional to 459 and 690

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Solution

The third proportional to 459 and 690 is: 1,037.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    459 : 690 = 690 : x
  2. Step 2: Convert to fraction form
    459/690 = 690/x
  3. Step 3: Cross multiply
    459x = 690 × 690
  4. Step 4: Simplify right side
    459x = 476,100
  5. Step 5: Solve for x
    x = 476,100/459
  6. Step 6: Final answer
    x = 1,037.25

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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.