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Finding the Fourth Proportional to 566.65, 782.36 and 409.56

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Solution

The fourth proportional to 566.65, 782.36 and 409.56 is: 565.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    566.65 : 782.36 = 409.56 : x
  2. Step 2: Convert to fraction form
    566.65/782.36 = 409.56/x
  3. Step 3: Cross multiply
    566.65x = 782.36 × 409.56
  4. Step 4: Simplify right side
    566.65x = 320,423.36
  5. Step 5: Solve for x
    x = 320,423.36/566.65
  6. Step 6: Final answer
    x = 565.47

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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.