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Finding the Fourth Proportional to 1,093.50, 1,640.25 and 409.50

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Solution

The fourth proportional to 1,093.50, 1,640.25 and 409.50 is: 614.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,093.50 : 1,640.25 = 409.50 : x
  2. Step 2: Convert to fraction form
    1,093.50/1,640.25 = 409.50/x
  3. Step 3: Cross multiply
    1,093.50x = 1,640.25 × 409.50
  4. Step 4: Simplify right side
    1,093.50x = 671,682.38
  5. Step 5: Solve for x
    x = 671,682.38/1,093.50
  6. Step 6: Final answer
    x = 614.25

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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.