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Finding the Third Proportional to 577.75 and 823.25

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Solution

The third proportional to 577.75 and 823.25 is: 1,173.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    577.75 : 823.25 = 823.25 : x
  2. Step 2: Convert to fraction form
    577.75/823.25 = 823.25/x
  3. Step 3: Cross multiply
    577.75x = 823.25 × 823.25
  4. Step 4: Simplify right side
    577.75x = 677,740.56
  5. Step 5: Solve for x
    x = 677,740.56/577.75
  6. Step 6: Final answer
    x = 1,173.07

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.