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Finding the Fourth Proportional to 564.20, 846.30 and 409.40

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Solution

The fourth proportional to 564.20, 846.30 and 409.40 is: 614.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    564.20 : 846.30 = 409.40 : x
  2. Step 2: Convert to fraction form
    564.20/846.30 = 409.40/x
  3. Step 3: Cross multiply
    564.20x = 846.30 × 409.40
  4. Step 4: Simplify right side
    564.20x = 346,475.22
  5. Step 5: Solve for x
    x = 346,475.22/564.20
  6. Step 6: Final answer
    x = 614.10

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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.