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Finding the Fourth Proportional to 413, 570 and 257.72

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Solution

The fourth proportional to 413, 570 and 257.72 is: 355.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    413 : 570 = 257.72 : x
  2. Step 2: Convert to fraction form
    413/570 = 257.72/x
  3. Step 3: Cross multiply
    413x = 570 × 257.72
  4. Step 4: Simplify right side
    413x = 146,900.40
  5. Step 5: Solve for x
    x = 146,900.40/413
  6. Step 6: Final answer
    x = 355.69

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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.