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Finding the Fourth Proportional to 457.82, 682.56 and 414.08

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Solution

The fourth proportional to 457.82, 682.56 and 414.08 is: 617.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    457.82 : 682.56 = 414.08 : x
  2. Step 2: Convert to fraction form
    457.82/682.56 = 414.08/x
  3. Step 3: Cross multiply
    457.82x = 682.56 × 414.08
  4. Step 4: Simplify right side
    457.82x = 282,633.59
  5. Step 5: Solve for x
    x = 282,633.59/457.82
  6. Step 6: Final answer
    x = 617.35

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.