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Finding the Fourth Proportional to 1,097.02, 1,643.36 and 823.42

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Solution

The fourth proportional to 1,097.02, 1,643.36 and 823.42 is: 1,233.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,097.02 : 1,643.36 = 823.42 : x
  2. Step 2: Convert to fraction form
    1,097.02/1,643.36 = 823.42/x
  3. Step 3: Cross multiply
    1,097.02x = 1,643.36 × 823.42
  4. Step 4: Simplify right side
    1,097.02x = 1,353,175.49
  5. Step 5: Solve for x
    x = 1,353,175.49/1,097.02
  6. Step 6: Final answer
    x = 1,233.50

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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.