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Finding the Third Proportional to 589.78 and 823.92

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Solution

The third proportional to 589.78 and 823.92 is: 1,151.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    589.78 : 823.92 = 823.92 : x
  2. Step 2: Convert to fraction form
    589.78/823.92 = 823.92/x
  3. Step 3: Cross multiply
    589.78x = 823.92 × 823.92
  4. Step 4: Simplify right side
    589.78x = 678,847.26
  5. Step 5: Solve for x
    x = 678,847.26/589.78
  6. Step 6: Final answer
    x = 1,151.02

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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.