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Finding the Fourth Proportional to 741.34, 1,023.01 and 409.78

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Solution

The fourth proportional to 741.34, 1,023.01 and 409.78 is: 565.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    741.34 : 1,023.01 = 409.78 : x
  2. Step 2: Convert to fraction form
    741.34/1,023.01 = 409.78/x
  3. Step 3: Cross multiply
    741.34x = 1,023.01 × 409.78
  4. Step 4: Simplify right side
    741.34x = 419,209.04
  5. Step 5: Solve for x
    x = 419,209.04/741.34
  6. Step 6: Final answer
    x = 565.47

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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.