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Finding the Fourth Proportional to 567.40, 782.10 and 409.72

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Solution

The fourth proportional to 567.40, 782.10 and 409.72 is: 564.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    567.40 : 782.10 = 409.72 : x
  2. Step 2: Convert to fraction form
    567.40/782.10 = 409.72/x
  3. Step 3: Cross multiply
    567.40x = 782.10 × 409.72
  4. Step 4: Simplify right side
    567.40x = 320,442.01
  5. Step 5: Solve for x
    x = 320,442.01/567.40
  6. Step 6: Final answer
    x = 564.76

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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.