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Finding the Fourth Proportional to 1,102.84, 1,653.70 and 409.48

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Solution

The fourth proportional to 1,102.84, 1,653.70 and 409.48 is: 614.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102.84 : 1,653.70 = 409.48 : x
  2. Step 2: Convert to fraction form
    1,102.84/1,653.70 = 409.48/x
  3. Step 3: Cross multiply
    1,102.84x = 1,653.70 × 409.48
  4. Step 4: Simplify right side
    1,102.84x = 677,157.08
  5. Step 5: Solve for x
    x = 677,157.08/1,102.84
  6. Step 6: Final answer
    x = 614.01

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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.