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Finding the Fourth Proportional to 652.53, 978.14 and 409.23

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Solution

The fourth proportional to 652.53, 978.14 and 409.23 is: 613.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    652.53 : 978.14 = 409.23 : x
  2. Step 2: Convert to fraction form
    652.53/978.14 = 409.23/x
  3. Step 3: Cross multiply
    652.53x = 978.14 × 409.23
  4. Step 4: Simplify right side
    652.53x = 400,285.26
  5. Step 5: Solve for x
    x = 400,285.26/652.53
  6. Step 6: Final answer
    x = 613.43

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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.