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Finding the Third Proportional to 584.50 and 823.88

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Solution

The third proportional to 584.50 and 823.88 is: 1,161.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    584.50 : 823.88 = 823.88 : x
  2. Step 2: Convert to fraction form
    584.50/823.88 = 823.88/x
  3. Step 3: Cross multiply
    584.50x = 823.88 × 823.88
  4. Step 4: Simplify right side
    584.50x = 678,770.02
  5. Step 5: Solve for x
    x = 678,770.02/584.50
  6. Step 6: Final answer
    x = 1,161.28

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.