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Finding the Fourth Proportional to 741.64, 1,023.50 and 410.07

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Solution

The fourth proportional to 741.64, 1,023.50 and 410.07 is: 565.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    741.64 : 1,023.50 = 410.07 : x
  2. Step 2: Convert to fraction form
    741.64/1,023.50 = 410.07/x
  3. Step 3: Cross multiply
    741.64x = 1,023.50 × 410.07
  4. Step 4: Simplify right side
    741.64x = 419,706.65
  5. Step 5: Solve for x
    x = 419,706.65/741.64
  6. Step 6: Final answer
    x = 565.92

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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.