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Finding the Fourth Proportional to 567.02, 782.34 and 409.70

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Solution

The fourth proportional to 567.02, 782.34 and 409.70 is: 565.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    567.02 : 782.34 = 409.70 : x
  2. Step 2: Convert to fraction form
    567.02/782.34 = 409.70/x
  3. Step 3: Cross multiply
    567.02x = 782.34 × 409.70
  4. Step 4: Simplify right side
    567.02x = 320,524.70
  5. Step 5: Solve for x
    x = 320,524.70/567.02
  6. Step 6: Final answer
    x = 565.28

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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.