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Finding the Fourth Proportional to 765.34, 1,056.20 and 416.04

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Solution

The fourth proportional to 765.34, 1,056.20 and 416.04 is: 574.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    765.34 : 1,056.20 = 416.04 : x
  2. Step 2: Convert to fraction form
    765.34/1,056.20 = 416.04/x
  3. Step 3: Cross multiply
    765.34x = 1,056.20 × 416.04
  4. Step 4: Simplify right side
    765.34x = 439,414.09
  5. Step 5: Solve for x
    x = 439,414.09/765.34
  6. Step 6: Final answer
    x = 574.14

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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.