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Finding the Fourth Proportional to 741.32, 1,023.01 and 409.75

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Solution

The fourth proportional to 741.32, 1,023.01 and 409.75 is: 565.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    741.32 : 1,023.01 = 409.75 : x
  2. Step 2: Convert to fraction form
    741.32/1,023.01 = 409.75/x
  3. Step 3: Cross multiply
    741.32x = 1,023.01 × 409.75
  4. Step 4: Simplify right side
    741.32x = 419,178.35
  5. Step 5: Solve for x
    x = 419,178.35/741.32
  6. Step 6: Final answer
    x = 565.45

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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.