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Finding the Third Proportional to 591 and 830

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Solution

The third proportional to 591 and 830 is: 1,165.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    591 : 830 = 830 : x
  2. Step 2: Convert to fraction form
    591/830 = 830/x
  3. Step 3: Cross multiply
    591x = 830 × 830
  4. Step 4: Simplify right side
    591x = 688,900
  5. Step 5: Solve for x
    x = 688,900/591
  6. Step 6: Final answer
    x = 1,165.65

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.