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Finding the Fourth Proportional to 765.74, 1,056.71 and 416.43

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Solution

The fourth proportional to 765.74, 1,056.71 and 416.43 is: 574.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    765.74 : 1,056.71 = 416.43 : x
  2. Step 2: Convert to fraction form
    765.74/1,056.71 = 416.43/x
  3. Step 3: Cross multiply
    765.74x = 1,056.71 × 416.43
  4. Step 4: Simplify right side
    765.74x = 440,038.38
  5. Step 5: Solve for x
    x = 440,038.38/765.74
  6. Step 6: Final answer
    x = 574.66

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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.