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Finding the Fourth Proportional to 1,102.66, 1,653.82 and 409.15

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Solution

The fourth proportional to 1,102.66, 1,653.82 and 409.15 is: 613.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102.66 : 1,653.82 = 409.15 : x
  2. Step 2: Convert to fraction form
    1,102.66/1,653.82 = 409.15/x
  3. Step 3: Cross multiply
    1,102.66x = 1,653.82 × 409.15
  4. Step 4: Simplify right side
    1,102.66x = 676,661.50
  5. Step 5: Solve for x
    x = 676,661.50/1,102.66
  6. Step 6: Final answer
    x = 613.66

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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.