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Finding the Fourth Proportional to 742.09, 1,024.05 and 410.50

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Solution

The fourth proportional to 742.09, 1,024.05 and 410.50 is: 566.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    742.09 : 1,024.05 = 410.50 : x
  2. Step 2: Convert to fraction form
    742.09/1,024.05 = 410.50/x
  3. Step 3: Cross multiply
    742.09x = 1,024.05 × 410.50
  4. Step 4: Simplify right side
    742.09x = 420,371.02
  5. Step 5: Solve for x
    x = 420,371.02/742.09
  6. Step 6: Final answer
    x = 566.47

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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.