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Finding the Fourth Proportional to 741.42, 1,023.06 and 409.84

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Solution

The fourth proportional to 741.42, 1,023.06 and 409.84 is: 565.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    741.42 : 1,023.06 = 409.84 : x
  2. Step 2: Convert to fraction form
    741.42/1,023.06 = 409.84/x
  3. Step 3: Cross multiply
    741.42x = 1,023.06 × 409.84
  4. Step 4: Simplify right side
    741.42x = 419,290.91
  5. Step 5: Solve for x
    x = 419,290.91/741.42
  6. Step 6: Final answer
    x = 565.52

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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.