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Finding the Fourth Proportional to 703.86, 971.42 and 409.14

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Solution

The fourth proportional to 703.86, 971.42 and 409.14 is: 564.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    703.86 : 971.42 = 409.14 : x
  2. Step 2: Convert to fraction form
    703.86/971.42 = 409.14/x
  3. Step 3: Cross multiply
    703.86x = 971.42 × 409.14
  4. Step 4: Simplify right side
    703.86x = 397,446.78
  5. Step 5: Solve for x
    x = 397,446.78/703.86
  6. Step 6: Final answer
    x = 564.67

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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.