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Finding the Fourth Proportional to 727.65, 1,004.11 and 412.92

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Solution

The fourth proportional to 727.65, 1,004.11 and 412.92 is: 569.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    727.65 : 1,004.11 = 412.92 : x
  2. Step 2: Convert to fraction form
    727.65/1,004.11 = 412.92/x
  3. Step 3: Cross multiply
    727.65x = 1,004.11 × 412.92
  4. Step 4: Simplify right side
    727.65x = 414,616.07
  5. Step 5: Solve for x
    x = 414,616.07/727.65
  6. Step 6: Final answer
    x = 569.80

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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.