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Finding the Fourth Proportional to 682.80, 1,024.25 and 410.64

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Solution

The fourth proportional to 682.80, 1,024.25 and 410.64 is: 615.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    682.80 : 1,024.25 = 410.64 : x
  2. Step 2: Convert to fraction form
    682.80/1,024.25 = 410.64/x
  3. Step 3: Cross multiply
    682.80x = 1,024.25 × 410.64
  4. Step 4: Simplify right side
    682.80x = 420,592.13
  5. Step 5: Solve for x
    x = 420,592.13/682.80
  6. Step 6: Final answer
    x = 615.98

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.