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Finding the Fourth Proportional to 1,102.55, 1,653.14 and 409.21

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Solution

The fourth proportional to 1,102.55, 1,653.14 and 409.21 is: 613.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102.55 : 1,653.14 = 409.21 : x
  2. Step 2: Convert to fraction form
    1,102.55/1,653.14 = 409.21/x
  3. Step 3: Cross multiply
    1,102.55x = 1,653.14 × 409.21
  4. Step 4: Simplify right side
    1,102.55x = 676,478.31
  5. Step 5: Solve for x
    x = 676,478.31/1,102.55
  6. Step 6: Final answer
    x = 613.56

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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.