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Finding the Fourth Proportional to 1,407.75, 2,111.41 and 823.02

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Solution

The fourth proportional to 1,407.75, 2,111.41 and 823.02 is: 1,234.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,407.75 : 2,111.41 = 823.02 : x
  2. Step 2: Convert to fraction form
    1,407.75/2,111.41 = 823.02/x
  3. Step 3: Cross multiply
    1,407.75x = 2,111.41 × 823.02
  4. Step 4: Simplify right side
    1,407.75x = 1,737,732.66
  5. Step 5: Solve for x
    x = 1,737,732.66/1,407.75
  6. Step 6: Final answer
    x = 1,234.40

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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.