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Finding the Fourth Proportional to 765.40, 1,056.26 and 416.09

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Solution

The fourth proportional to 765.40, 1,056.26 and 416.09 is: 574.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    765.40 : 1,056.26 = 416.09 : x
  2. Step 2: Convert to fraction form
    765.40/1,056.26 = 416.09/x
  3. Step 3: Cross multiply
    765.40x = 1,056.26 × 416.09
  4. Step 4: Simplify right side
    765.40x = 439,494.98
  5. Step 5: Solve for x
    x = 439,494.98/765.40
  6. Step 6: Final answer
    x = 574.20

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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.