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Finding the Third Proportional to 569.81 and 684.84

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Solution

The third proportional to 569.81 and 684.84 is: 823.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    569.81 : 684.84 = 684.84 : x
  2. Step 2: Convert to fraction form
    569.81/684.84 = 684.84/x
  3. Step 3: Cross multiply
    569.81x = 684.84 × 684.84
  4. Step 4: Simplify right side
    569.81x = 469,010.96
  5. Step 5: Solve for x
    x = 469,010.96/569.81
  6. Step 6: Final answer
    x = 823.10

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.