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Finding the Fourth Proportional to 1,102.69, 1,653.98 and 409.08

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Solution

The fourth proportional to 1,102.69, 1,653.98 and 409.08 is: 613.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102.69 : 1,653.98 = 409.08 : x
  2. Step 2: Convert to fraction form
    1,102.69/1,653.98 = 409.08/x
  3. Step 3: Cross multiply
    1,102.69x = 1,653.98 × 409.08
  4. Step 4: Simplify right side
    1,102.69x = 676,608.09
  5. Step 5: Solve for x
    x = 676,608.09/1,102.69
  6. Step 6: Final answer
    x = 613.60

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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.