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Finding the Fourth Proportional to 698.17, 1,047.39 and 409

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Solution

The fourth proportional to 698.17, 1,047.39 and 409 is: 613.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    698.17 : 1,047.39 = 409 : x
  2. Step 2: Convert to fraction form
    698.17/1,047.39 = 409/x
  3. Step 3: Cross multiply
    698.17x = 1,047.39 × 409
  4. Step 4: Simplify right side
    698.17x = 428,382.51
  5. Step 5: Solve for x
    x = 428,382.51/698.17
  6. Step 6: Final answer
    x = 613.58

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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.