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Finding the Fourth Proportional to 565.84, 780.42 and 409.06

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Solution

The fourth proportional to 565.84, 780.42 and 409.06 is: 564.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    565.84 : 780.42 = 409.06 : x
  2. Step 2: Convert to fraction form
    565.84/780.42 = 409.06/x
  3. Step 3: Cross multiply
    565.84x = 780.42 × 409.06
  4. Step 4: Simplify right side
    565.84x = 319,238.61
  5. Step 5: Solve for x
    x = 319,238.61/565.84
  6. Step 6: Final answer
    x = 564.19

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.